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MATEMATİK YILLIK ÖDEVİ

 

 

 

Adı                  :       Gökhan

 

Soyadı             :       ASLAN

 

Öğretmen        :       Harun KARATOSUN

 

Konu               :       Fonksiyonlar

 

 

 

 

 

 

1.           f: A       B

              A: {1,2,3,4,5} ve B = {x,y} ise A ’dan B ’ye kaç tane fonksiyon tanımlanır?

             

              A) 10       B) 25       C) 32         D) 46         E) 50

 

2.                      f(1) = 3 ; f(x+1) = f(x) – 1 ise f(4) kaçtır?

 

A) 5         B) 4         C) 3            D) 1           E) 0

-1

 
 


3.           f: R       R ;  f    (3) = 5 ise f(5) kaçtır?

             

              A) 0         B) 1         C) 2            D) 3           E) 5      

 

4.           f(x) = 2x + 4 ve f(x) + f(y) = 18 ise x+y kaçtır.

 

              A) 2         B) 3         C) 4            D) 5           E) 6

 

5.           f: A        B  s(A) = 3  s(B) = 7 ise A ’dan B ’ye kaç

3

 

7

 
              tane 1:1 fonksiyon tanımlanır?

             

              A) 3                          B) 7                          C) 180

             

              D) 200                     E) 210

 

6.                      f(ab) = f(a) + f(b) ise f(1) kaçtır?

 

A) 0         B) 1         C) 2            D) 3           D) 4

 

7.                      f(x+4) = x 2 f(x+3) ve f(5) = 3 ise f(6) kaçtır?

 

A) 12                        B) 14                         C) 16

             

              D) 18                       E) 24

 

8.                      Aşağıdakilerden hangisi örtendir?

 

              A) f: N         Z ; f(x) = 2x-1

             

              B) f: Z       R ; f(x) = 5x – 4

             

              C) f: Z       Z ; f(x) = 3x + 1

             

              D) f: R       R ; f(x) = 2x – 5

             

              E) f: N       N ; f(x) = 5x + 3

             

 

9.           f(x) doğrusal bir fonksiyondur.

             

              f(2) =7 ve f(5) =4 ise f(1) kaçtır?

             

              A) 10       B) 9         C) 8            D) 7           E) 6

 

10.         n bir reel sayı ve  n.f(n+1) – f(n) = 0

             

              f(5) = 11 ise f(3) kaçtır?

             

              A) 132     B) 120     C) 96         D) 64         E) 22

 

11.         f: R     R,   f(2x -1) = 6x + 1 ise  f  -1  (-5) kaçtır?

             

              A) -3                         B) -2                             C) 2

             

              D) 3                          E) 6

 

12.                  A = {1,2,3,4,5} ve B = {a,b,c} ise A ’dan B ’ye

 

kaç tane 1:1 olmayan fonksiyon tanımlanır?

             

              A) 60                        B) 124                          C) 163

             

              D) 183                     E) 243

 

3x-2

   5

 
13.         f(x) =             ise f -1   (-2) kaçtır?

             

  8

  3

 

  1

  2

 
             

  5

  7

 
              A)                             B) -3                             C)

 

             

              D) -5                        E)

 


14.         f: R - {       }               R - {       }

             

              f(x) =             ise     f -1 ( 3 ) kaçtır?

 

             

              A) 2         B) 5         C) 6            D) 13         E) 18

 

15.         f(x) = 2x-1 ;  (gof) (x) = 3x - 5 ise g -1 (1) kaçtır?

 

              A) 1                          B) 3                               C) 6

             

              D) 9                          E) 12

 

16.                  (fof)(x) = 9x-5 ise f(x) = 1 denkleminin çözüm

 

kümesi hangisidir?

 1 , 3

 2   2

 

 1 , 3

 2   4

 
 


A) {             }                                B) {            }

 

   1 ,   3

   2     2

 

 1 , 3

 4   2

 
             

C) {               }                             D) {            }

 1 ,    3

 4      2

 
             

              D) {             }

 

 

 

17.         f: A       B,  f(x) = -5x + 3 için A = (2,3] ise B hangisidir?

 

              A) [-12, 7]                B) [-12, -7) C) (-12, 7)

             

              D) [-12, 7)                E) (12, -7]

 

18.         f: R      R, f(x) = x² -4x-5 olduğuna göre;  f ( (0,6])

             

              aşağıdakilerden hangisidir?

 

              A) (-5, 7]                  B) (-9, 7)                       C) [-5, 7)

             

              D) [-9, 7]                  E) (-9, -7)

 

19.         f: R       A, f(x) = Ix-5I + 3 fonksiyonunun örten

             

              olması için A hangisidir?

 

              A) R                          B) [2, +   )                     C) [5, +   )

             

              D) [3, +   )                E) R + U{0}

 

ax-3

   5

 
 


20.         f(x) =              fonksiyonunda f ;  1:1 örten olup

             

              f(x) = f -1(x) olması için a kaç olmalıdır?

1

3

 
 


 1

 5

 
              A) -5        B) 5         C)               D) 3           E)

 

 

 

21.         f: Z      N ; a = 0 ; f(x) = ax - b örten olması için

             

              a kaç olmalıdır?

             

              A) -1        B) 1         C) +1         D) 2           E) +2

 

 

 

22.         f: R-1 – {-8}        R – {1}

x + 1

x + 2

 
             

x + 5

x + 8

 
              f(3x - 2) =            ise       f -1 (x) hangisidir?

 

5 - 8x

 x - 1

 
             

3x -5

 x - 1

 
              A) f -1(x) =                                   B) f    (x) =

 

8x -5

 x + 8

 
             

3x -5

 x - 1

 

x - 1

x + 8

 
              C) f    (x) =                                  D) f    (x) =

 

 

              E) f    (x) =

 

3

2

 
 


3

5

 
23.         f(x) =             ise     f -1(      )     kaçtır?

 

 

6

5

 

5

4

 

7

3

 

4

7

 
              A)             B)             C)               D)               E)

 

 

x+2

 
24.         f(x) = 3x   + 3 x+2       ise f -1 (810)  kaçtır?

 

              A) 3         B) 4         C) 9            D) 10         E) 81

 

25.         f(x) = 2x-1             (fofof) (x) kaçtır?

             

              A) 4x-1                     B) 6x-4                         C) 8x-7

             

              D) 12x-9                  E) 16x-15

 

26.                  f(x) = 3x -5 (gof)(x) = 5x - 4 ve;

             

              g(2) + g -1  (x) = 1           x kaçtır?

 

              A)                             B)                                  C)

             

             

              D)                             E)

 

27.                  f = {(0,3), (1,5), (5,-2), (3,7)} için,

 

f2   , aşağıdakilerden hangisidir?

             

              A)  {(0,9), (1,25), (5,4), (3,49)}

             

              B)  {(0,9), (1,25), (5,4), (3,21)}

             

              C)  {(0,3), (1,5), (25,-2), (9,7)}

             

              D)  {(0,9), (1,5), (5,4), (3,7)}

             

E)    {(0,3), (1,5), (5,-2), (3,7)}

 

 

28.                  f = {(1,3), (-2,5), (3,2), (0,7)}

             

              g = {(1,6), (2,5), (3,7), (0,1)} ise,

             

              f + g hangisidir?

             

              A) f+g = {(1,9), (3,9), (0,8)}

             

              B) f+g = {(1,9), (0,8), (-2,5)}

             

              C) f+g = {(1,9), (-2,10), (3,9)}

             

              D) f+g = {(1,3), (2,7), (3,5)}

             

              E) f+g = {(1,9), (-2,7), (0,8)}

 

 

 

 


29.         f = (                )      g = (              )

             

              ise fog hangisidir?

             

              A) (               )           B) (               )

             

             

              C) (                )          D) (                  )

                              

              E) (                  )

 

 

30.         A = {1, 2, 3, 4} kümesinin f = (                 )

                              

              g = (                  ) permütasyonları veriliyor.

             

              f ox = g   ise x hangisidir?

             

              A) (                )                B) (              )

             

             

              C) (                )              D) (              )

             

-1

 
             

              E) (                 )

             

31.                  Aşağıdakilerden hangisi çift fonksiyon

 

değildir?

 

              A) f(x) = cosx + I5xI – 8

 

B) f(x) = x4   - x 2  + 3

 

 


C) f(x) =

                                          

D) f(x) = x 2 +3x   - tanx

 

E) f(x) = (x  +3x) sinx

 

32.                  ( 2x – y , 5 ) = (1 , x + y ) ise x.y2 - x  değeri kaçtır?

 

A) 1         B) 2         C) 3            D) 4           E) 5

 

33.         ( x  + y  ,5 ) = ( 2xy + 1 , x + y) ve x > y >0 ise x 

             

              kaçtır?

             

              A) 1         B) 2         C) 4            D) 16         E) 9

             

34.         (2x + 1, 3 – y,  2 - 3) = (7, 1, 1) olduğuna göre,

                              

              x+y+z  toplamı kaçtır?

             

              A) 6         B) 7         C) 8            D) 9           E) 11

             

 

 

 

35.               

 

 

 

 
{1,2,3} Kümesinden {a,b,c} kümesine aşağıdaki fonksiyonlar tanımlanıyor. Bu fonksiyonlardan hangisinin ters fonksiyonu vardır ?

 

A)    {(1,a),(2,a),(3,c)}

 

B)    {(1,b),(2,b),(3,b)}

 

C)    {(1,c),(2,a),(3,b)}

 

D)    {(1,b),(2,c),(3,b)}

 

E)   {(3,a),(2,b),(1,a)}

 

 

 

 

 

36.        f(3x +1) = 2x² + x + 5 olduğuna göre, f(-2)

 

aşağıdakilerden hangisine eşittir?                           

             

              A) 7         B) 6         C) 5            D) 4           E) 3

 

 

 

 

37.        f(x)= 2x+3 ise f(x-2) aşağıdakilerden hangisine

 

eşittir?

             

              A) 2x+7                    B) 2x+1                        C) 2x+5

             

              D) 2x-1                    E) 2x-5

 

 

 

 
 


38.         f(2x + 1) = x² + 1 olduğuna göre, f(x) aşağıdakilerden

             

              hangisidir?

             

              A)                             B)

             

              C)                             D)

             

              E)

 

 

 


39.         f(x) =             fonksiyonu için f -1(a) = 4 olması için a ne olmalıdır ?

             

              A) 3         B)             C)               D) 5           E) –3

             

 

 

 

 


40.         f -1 og -1    = (                 )    ve   f = (                   )

-1

 
 


              ise g    aşağıdakilerden hangisidir?

             

              A) (                  )                          B) (                   )

             

             

              C) (                 )                           D) (                 )

             

 

              E) (                   )

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C E V A P L A R

 

 

 

 

 

 

 

5

 
1.           s(A) = 5 ve s(B) = 2 ise 2   = 32 tane

             

                        Cevap C

             

2.           x = 1          f(2) = f(1) - 1         f(2) = 2

             

              x = 2          f(3) = f(2) - 1         f(3) = 1

             

              x = 3          f(4) = f(3) - 1         f(4) = 0

             

                                                                                Cevap E

 

-1

 

-1

 
3.           f    (a) = b         f(b) = a

             

              f    (3) = 5         f(5) = 3

             

                                                                                Cevap D        

 

4.                      2x + 4 + 2y + 4 = 18

             

              2(x + y) = 10        x +y = 5

                                                                               

                                                                                Cevap D

 


5.           p(n,r) tane             =      = 5.6.7 = 210

             

             

                                                                     Cevap E

 

6.           a = 1 ise f(b) = f(1) + f(b)

             

                                         f(1) = 0

 

                                                                                Cevap A

 

7.           x = 2          f(6) = 4.f(5) = 4.3

             

                                f(6) = 12

 

                                                                                Cevap A

 

 

 

 

 

 

 

8.           f : A          B örten olması için s(A)>s(B) olmalı.

             

              Bu özellik D ve E şıklarında var.

y-3

  5

 
             

y+5

  2

 

y-5

  2

 
              E de y = 5x + 3         x =       E Z olduğundan örten

             

              olamaz. Ancak D) de ise y=2x-5         x =       

             

              V yE R için x =      E R dir.

             

                                                           Cevap D

           

 

 

9.                 f(x) = ax + b olup

                       

              f(2) = 2a + b = 7

             

              f(5) = -5a + b = -4

                  __

             

             

              -3a=3           a=-1 ve b=9

 

              f(x)= -x+9           f(1)=-1+9=8

 

                                                                                  Cevap C

 


10.         n=4            4.f(5)= f(4)

 


              n=3            3.f(4)= f(3)

 

 


                        12.f(5) = f(3)

 

                        12.11= f(3)            f(3) = 132

 

                                                                                  Cevap A

 


11.         f(x) = 6.              +1=3x+4 

 

-1

 
 


              f    (x) =                          f   (-5) = -3

 

                                                                                  Cevap A

5

 
 


12.         A dan B ye 3   tane fonksiyon vardır.

5!

2!

 
 


              Bunlardan P (5,3) =          =3.4.5 = 60 tanesi

 

              1:1 dir. O halde 1:1 olmayan fonksiyonların sayısı

5

 
 


              3  -60=243-60 = 183

                                                                                  Cevap D

5x+2

   3

 

-10+2

     3

 

8

3

 

-1

 

-1

 
 


13.         f    (x) =                           f     (-2)=              = -

 

6

1

 

X+3

2x-5

 
                                                                                  Cevap C

-1

 

-1

 
 


14.         f    (x) =               f    (3) =          =6

 

                                                                                  Cevap C

 

15.         (gof) (x) = 3x-5 ise

 

              g(f(x)) = 3x-5           f(x) 2x-1 olduğundan

-1

 

X+1

  2

 

X+4

   2

 
 


              f    (x) =                                            g (x) = 3             -5

 

 

3x-7

   2

 

-1

 

2x+7

   3

 
 


              g(x) =            ise g   (x) =          

             

-1

 
 

             g  (1) = 3

 

                                                                                  Cevap B

 

16.         f(x) = ax + b olsun. (fof) (x) = 9x-5

 


              f(f(x)) = 9x-5                                    f (ax+b) = 9x-5

 


                                                                       a (ax+b) +b = 9x-5

 

 
                                   a² x + ab + b = 9x-5 olduğundan polinomların

 

              eşitliği tanımı gereğince

2

 
 


              a  = 9                a =   3 ve ab+b = -5 olduğundan

5

4

 
 


              a = 3                3b+b = -5                 b= -

5

2

 
                                                                                                          dir.

              a = -3                  -2b = -5                  b=          

9

4

 

5

4

 
 


3

4

 
              O halde f(x) = 3x-       =1                    3x =

 


                                                                             x =

5

2

 

5

2

 
 


              f(x) = -3x +       = 1   -3x = 1-           

 

1

2

 
 


                                                             -3x = -                 x=              

1    ,  3

2       4

 
 


              Ç =

                                                                                  Cevap B

17.         2 <  X  <  3

 

              -5.2  > -5x  >  -5.3

 

              -10  > -5x >  -15

 

              -10+3 >  -5x+3  > -15+3

 

              -7  > -5x+3 > -12

 

              -12   <  -5x + 3   < -7

 

                                                                                  Cevap B

 b

2a

 

4

2

 
 


18.         -         =          = 2

 

              f(0) =-5

             

              f(2) = 2 ² -4.2 – 5 = -9

 

              f(6) = 6²   -4.6 – 5 = 7

 

              f((0,6]) = [-9.7]

 

                                                                                  Cevap D

 


19.         y= I x-5 I + 3             I x-5 I = y-3

 

              örten olması için   V  yE A için xE R olmalıdır. O

 

              halde y  > 3 için I x-5 I tanımlı olacağından [3, +oo )

 

              olmalıdır.

 

                                                                                  Cevap D

-1

 

5x+3

   a

 

--1

 
 


20.         f    (x) =                  ve f(x) = f   (x)

 

              ise a=-5 olmalıdır.

5x+3

   a

 

-ax+3

  -5

 
 


                              =                                       =

 

              polinomların eşitliğinden a = -5 dir.

 

                                                                                  Cevap A

 

 

 

 

 y+b

  a

 
21.      y = ax-b               x =

 y+b

  a

 
 


         V yE N için x =           E Z olması için a =   ±1 olmalıdır.

 

 x+2

   3

 
                                                                                  Cevap C

 x+5

 x+8

 
 

 


 x+2

   3

 
22.         f(x) =                        =                  ise

-1

 

-1

 

5-8x

 x-1

 
 

 

 


              f   (x) =                           f    (x) =

 

                                                                                  Cevap B

-1

 

7

3

 
 

 


3

2

 
23.         f    (x) =                          f                   =                      =

 

 

 


                                                                                  Cevap C

 

 y

10

 

3

 

x

 
24.         y = 10.3                 x = log         

-1

 

 x

10

 

-1

 
 


3

 

3

 
              f   (x) =   log                         f   (810) = log

 

4

 
 


3

 
                                                                            = log 3   = 4

 


                                                                                  Cevap B

25.         (fof) (2x-1) = f(2(2x-1) –1)

 

              (fofof) (x)   = 2(4x-3) -1

 

                                  =8x-7

                                                                                  Cevap C

 x+5

   3

 
 


26.         g(3x-5) = 5x-4            g(x) = 5.            -4

5x+13

    3

 

-1

 

3x-13

    5

 
 


              g(x) =                          g  (x) =                   

 

5.2+13       

      3

    

 

23

 3

 
             

             g(2) =                 =   

 

-1

 

61

 9

 
 


              g(2) + g   (x) = 1 ise              +              = 1              x = -

 

                                                                                  Cevap A

2

 

n

 
 


27.         f   = [f(x)]     olduğundan;

 


              f   =     (0,9) , (1,25) , (5,4) , (3,49)    dir.

 

                                                                                  Cevap A

 


28.         f + g =    (1,9) , (3,9) , (0,8)     dir.

 

                                                                                  Cevap A

 

29.         Fonksiyonların bileşkesinde aynı yol izlenir.

 


              fog =                         

                                                  °

 

 


                    =    

                                                                                  Cevap D

 


30.         f =                                    f   =  

-1

 

-1

 
 


              f   ox = g              fof     ox = fog

 

                                           Iox = fog                   x = fog

 

              O halde,

 


              x =                     

                                            °

 

 


                 = 

 

                                                                                  Cevap B

 

31.         D) f(x) = Ç + Ç – T = T olduğundan,

 

                                                                                  Cevap D

2

 
 


2

 
32.         2x-y = 1                               2x-y=1                        x.y-x  =

 


               x+y = 5                               2.2-y=1                      2.3-2  =

   +

              3x = 6                                  y=3                             6-4 = 2

             

               x = 2                                                           Cevap B

 

 

 


33.         x² +y²   = 2xy+1                   (5-y)²  + y²   = 2. (5-y).y+1

 


              x+y = 5                                25-10y+ y² +y²   =10y-2y²   +1

 

 
 


              x=5-y                                   4y² -20y+24=0

 

 
 


                                                           y² –5y+6 =0

 

                                                           (y-2) (y-3) = 0

 

                                                             -6y+y = -6

 

 

 

y

 
                                                           y = 2

 

                                                           x = 3               x  = 3²  = 9

 

                                                                                  Cevap E

 

34.         2x+1 = 7                  2x = 6             x = 3

 

              3-y = 1                     -y = -2             y = 2

 

 
 


                -3 = 1                   = 4             z = 2

 

              x+y+z = 3+2+2= 7

 

                                                                                  Cevap B

35.         A, B, D, E şıklarında 1:1 ve örten fonksiyon vardır.

 

              C şıkkında ise ters fonksiyondur.

 

                                                                                  Cevap C

2

 
 


36.         3x+1 = -2                 f(3x+1) = 2x +x+5

2

 
 


              3x = -3                     f(-2) = 2(-1)  + (-1) + 5

 

              x = -3                               = 6

 

                                                                                  Cevap B

 

37.         f(x) = 2x+3

 

              f(x-2) = 2 (x-2) +3

 

                        = 2x-4+3

 

                        = 2x-1

 

                                                                                  Cevap D

2

 
 


2

 
38.         f(2x+1) = x  +1

 


               f(x) =             +1

 

 


               f(x) =                    +

 

 


               f(x) =

 

 


               f(x) =

 

5x+1

2x-3

 

3x+1

2x-5

 

-1

 
                                                                                  Cevap A

 

39.         f(x) =                       f   (x) =

 

-1

 

5x+1

2x-3

 

-1

 
 


               f  (x) =                   = 4         f   (x) =5x+1 = 8x-12

-1

 
 


                                                           f   (x) = -3x = -13

13

 3

 
 


                                                           x =

 

                                                                                  Cevap C

-1

 
 


1 2 3 4

2 3 4 1

 

1 2 3 4

4 3 1 2

 

-1

 
40.         f   og of =                      

                                                °

 

 

 


              f  og  of =

 

 

                                                                                  Cevap B