Composition

First, evaluate  f(4)  =  3(4)^2 - 7  =  48 - 7  =  41

Then evaluate f(-4) = 3(-4)^2 - 7 = 48 - 7 = 41

So    g(f(4)) = g(41) = 9

So...it  must also be that  g(f(-4)) = g(41)  = 9

Solution:

This is very simple. 

\(f(x) = 3(x^2 ) - 7\), so \(f(4) = 3(4^2) - 7 = (3*16) - 7 = 48 - 7 = 41\).

We know that \(g(f(4)) = 9\) so this means that \(g(41) = 9\).

\(f(-4) = 3 (-4^2) - 7\) and since \(-4^2 = -4 * -4 = 16\), this is the same thing as \(f(4)\) so \(f(-4)\) also equals \(41\).

We know that \(g(41) = 9\) thus \(g(f(-4)) = 9\) as well.

\(\boxed{g(f(-4) = \boxed{9}}\)

RB - ∃\(\)