Given f(x) = 2x^3 + x^2f(x)=2x3+x2 and g(x) = 7x - 2g(x)=7x2 how do you find (gf)(3)?

1 Answer
May 23, 2018

g(f(3))=439g(f(3))=439

Explanation:

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)=7x2

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+7x22

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)22

=>=14(27)+7(9)-2=14(27)+7(9)2

=>=378+63-2=378+632

=>441-24412

g(f(3))=439g(f(3))=439

Hope this helps!