Question

I need help with this calculus problem

Answer 1

This is a composite function, we apply the chain rule to differentiate,

$f(g(x))'=f'(g(x))\times g'(x)$

At $x=4$

$f(g(4))'=f'(g(4))\times g'(4)$

$f(g(4))'=f'(3)\times g'(4)$

$f(g(4))'=8\times(-4)$

$f(g(4))'=-32$

The correct answer is option C

Answer 2

First, find the value of g(x) at x=4:  it's 3.

Next, use this result, 3, as the input to f(x):  f(3) = 1

So f(g(4)) = 1.