Question

G ο f = 2x² + 4x - 3
f (x) = x+ 5
g (x) = ...?

Answer 1

Gof(x) = g(f(x))
2x² + 4x - 3 = g(x+5)         ⇒ x+5 = a , x = a-5
2(a-5)² + 4(a-5) - 3 = g(a)
2(a²-10a+25) + 4a - 20 - 3 = g(a)
2a² - 20a + 50 + 4a - 20 - 3 = g(a)
2a² - 16a + 27 = g(a)

jadi g(x) = 2x² - 16x + 27