To find g(f(3))g(f(3)), we need to find g(f(x))g(f(x)) first.
g(x)g(x) is our outside function, so we'll start with that first.
color(blue)(g(x)=7x-2)g(x)=7x−2
Wherever we see an xx, we'll replace it with color(red)(f(x))f(x). We get
g(f(x))=color(blue)(7color(red)((2x^3+x^2))-2g(f(x))=7(2x3+x2)−2
which further simplifies to
g(f(x))=14x^3+7x^2-2g(f(x))=14x3+7x2−2
To find g(f(3))g(f(3)), we just have to plug 33 in for xx. We get
g(f(3))=14(3)^3+7(3)^2-2g(f(3))=14(3)3+7(3)2−2
=>=14(27)+7(9)-2⇒=14(27)+7(9)−2
=>=378+63-2⇒=378+63−2
=>441-2⇒441−2
g(f(3))=439g(f(3))=439
Hope this helps!