Question

What is (f⋅g)(x)? f(x)=x^2−3x+2 g(x)=x^3−8 Enter your answer, in standard form, in the box. (f⋅g)(x)=

Answer 1

Answer:

$f(g(x))=x^{6}-19x^{3}+90$

Step-by-step explanation:

We have been given the following equations;

f(x)=x^2−3x+2

g(x)=x^3−8

We are required to determine the composite function (f⋅g)(x). This simply means that we shall substitute the function g(x) in place of x in the function f(x);

$f(g(x)) = g(x)^{2}-3g(x)+2\\\\f(g(x))=(x^{3}-8)^{2}-3(x^{3}-8)+2\\\\f(g(x))=x^{6}-16x^{3}+64-3x^{3}+24+2\\\\f(g(x))=x^{6}-19x^{3}+90$