Question

Bantu jawab soal nomor 7 & 8 dengan cara....

Answer 1

7) g(x) = 2x + 3
(f o g)(x) = 4x^2 + 10x + 11
f(g(x)) = 4x^2 + 10x + 11
f(2x + 3) = 4x^2 + 10x + 11
Misal 2x + 3 = a => 2x = a - 3 => x = (a - 3)/2
f(a) = 4[(a - 3)/2]^2 + 10(a - 3)/2 + 11
f(a) = 4(a^2 - 6a + 9)/4 + 5(a - 3) + 11
f(a) = a^2 - 6a + 9 + 5a - 15 + 11
f(a) = a^2 - a + 5
f(x) = x^2 - x + 5

8) f(x) = (x - 1)/(2x + 2)
(x - 1)/(2x + 2) = y
x - 1 = 2xy + 2y
x - 2xy = 2y + 1
x(1 - 2y) = 2y + 1
x = (2y + 1)/(1 - 2y)
f^-1(x) = (2x + 1)/(1 - 2x) ; x ≠ 1/2