Question

Tolong bantu
diketahui f(x)= 1-2x dan (gof)(x)= 4x²-6x+3 tentukan rumus fungsi g(x) nilai (fog) (4)

Answer 1

Verified answer

Fungsi Komposisi
Kelas XI

f(x) = 1 - 2x

(g o f)(x) = 4x² - 6x + 3
g(f(x)) = 4x² - 6x + 3
g(1 - 2x) = 4x² - 6x + 3

Misal a = 1 - 2x
Maka x = (1 - a) / 2

g(a) = 4( [1 - a] / 2)² - 6( [1 - a] / 2) + 3
g(a) = 4 ( [1 - a]² / 4 ) - 3(1 - a) + 3
g(a) = 1 - 2a + a² - 3 + 3a + 3
g(a) = a² + a + 1
g(x) = x² + x + 1
___________________________

g(4) = 4² + 4 + 1
g(4) = 21

(f o g)(4) = f(g(4))
= f(21)
= 1 - 2(21)
= 1 - 42
= -41