Question

Let f: (–1, 1) → R be a differentiable function with f(0) = –1 and f'(0) = 1. If g(x) = [f(2f(x) + 2)]², then g'(0) = ______.

Options

• 0

• –2

• 4

• –4

Answer 1

Let f: (–1, 1) → R be a differentiable function with f(0) = –1 and f'(0) = 1. If g(x) = [f(2f (x) + 2)]², then g'(0) = –4.

Explanation:

g(x) = [f(2f(x) + 2)]² 

∴ g'(x) = 2[f(2f(x) + 2)] . [f(2f(x) + 2)]' = 2 [f(2f(x) + 2] f'[2f (x) + 2] . 2f'(x)

∴ g'(0) = 2[f(-2 + 2)] f'[-2 + 2]. 2(1)

= 2[f(0)] [f'(0)] 2

= 2(–1)(1)2 = – 4