Question

Let F(x) = f(f(x)) and G(x) = (F(x)) ^ 2 . You also know that f(3) = 2 , f(2)=3, f^ prime (2)=7 , f^ prime (3)=11

Answer 1

From the information given,

F(x) = f(f(x)

G(x) = (F(x))^2

F'(x) = f'(f(x)) * f'(x)

F'(3) = f'(f(3)) * f'(3)

f'(f(3)) = f'(2) = 7

f'(3) = 11

F'(3) = 7 * 11

F'(3) = 77

G'(x) = 2F(x) * F'(x) = 2f(f(x) * F'(x)

G'(3) = 2F(3) * F'(3) = 2f(f(3) * F'(3)

Given,

f(f(3) = f(2) = 3

G'(3) = 2 * 3 * 77

G'(3) = 462