Question

I need help with this question plsss

Answer 1

In standard form, the answer is
`(f*g)(x)=x^(6)+6x^(4)+8x^(2)+2`.

Explanation:

`(f*g)(x)` is the same as saying
`f(g(x))`.

Simply put, sub into
`f(x)` using the definition of
`g(x)` as an x-value.

`f(x)=x^(3)-4x+2\\g(x)=x^(2)+2\\\\(f*g)(x)=f(g(x))\\\\(f*g)(x)=(x^(2)+2)^(3)-4(x^(2)+2)+2\\(f*g)(x)=[ (x^(2)+2)(x^(2)+2)(x^(2)+2) ] -4x^(2)-8+2\\(f*g)(x)=[ (x^(4)+4x^(2)+4)(x^(2)+2)]-4x^(2)-6\\(f*g)(x)=x^(6)+6x^(4)+12x^(2)+8-4x^(2)-6\\(f*g)(x)=x^(6)+6x^(4)+12x^(2)-4x^(2)+8-6\\(f*g)(x)=x^(6)+6x^(4)+8x^(2)+2`