Question

21. Diketahui f(x) = x2 – 25 dan g(x) = x + 5 maka (fog) (x) = … .

A x2 – 10x

B x2 – 20x

C x2 + 20x

D x2 + 10x

E x2 – 20


23. Diketahui f(x) = 3x – 2 dan (gof) (x) = 7 – 6x , maka g(-1) = … .

A 1

B 2

C 3

D 4

E 5


24. Jika f(x) = x, g(x) = x + 1 dan h(x) = x + 2, maka (fogoh)(x) = … .

A x + 5

B x + 3

C x + 2

D x – 3

E x – 4


25.Jika (fog)(x) = 2x/(x+3) dan f(x) = x + 1 maka g(x) = … .

A x/(x+3)

B (2x-3)/(x+3)

C (3x+3)/(x+1)

D (3x-3)/(x+3)

E (3x+3)/(-x+1)

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Answer 1

Penjelasan dengan langkah-langkah:

21) D

f(x) = x² – 25

g(x) = x + 5

(f o g)(x) = f(x + 5)

(f o g)(x) = (x + 5)² – 25

(f o g)(x) = x² + 10x + 25 – 25

(f o g)(x) = x² + 10x

23) E

f(x) = 3x – 2

(gof) (x) = 7 – 6x

g(3x – 2) = 7 – 6x

g(x) = 7 – 6(⅓[x+2])

g(x) = 7 – 2x – 4

g(x) = 3 – 2x

maka g(–1) = 3 – 2(–1)

g(–1) = 3 + 2

g(–1) = 5

24) B

f(x) = x

g(x) = x + 1

h(x) = x + 2

maka,

(fogoh)(x) = f o g(x+2)

(fogoh)(x) = f(x + 3)

(fogoh)(x) = x + 3

25) F

(fog)(x) = 2x/(x+3)

f(x) = x + 1

g(x) + 1 = 2x/(x + 3)

g(x) = 2x/(x + 3) – 1

g(x) = 2x/(x + 3) – (x + 3)/(x + 3)

g(x) = [ 2x – x – 3 ]/(x + 3)

g(x) = (x – 3)/(x + 3)