Answer:
[tex]f(g(x))=x^{6}-19x^{3}+90[/tex]
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);
[tex]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[/tex]
