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

`f(g(x))=x^(6)-19x^(3)+90`

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`