Jika f:R =>R dan g:R=>R dengan (fog)(x)=3x^2+6x-9 dan g(c) =x+1 carilah a. f(x) b. (F^-1og^-1) (x) Mohon bantuannya kak

KOMPOSISI FUNGSI

a.
f(g(x)) = 3x^2 + 6x - 9
f(x + 1) = 3x^2 + 6x - 9
f(x + 1) = 3x^2 + 6x + 3 - 12
f(x + 1) = 3(x^2 + 2x + 1) - 13
f(x + 1) = 3(x + 1)^2 - 13
misal y = x + 1
f(y) = 3y^2 - 13

sehingga
f(x) = 3x^2 - 13

b.
=> (g○f)(x)
=> g(f(x))
=> g(3x^2 - 13)
=> (3x^2 - 13) + 1
=> 3x^2 - 12

(gof)(x) = y
3x^2 - 12 = y
3x^2 = y + 12
x^2 = (y + 12)/3
x = akar((y + 12)/3)
(g○f)-1(x) = akar((x + 12)/3)
(f-1○g-1)(x) = akar((x + 12)/3)