STEP - BY - STEP EXPLANATION
What to find?
(f x g)(x)
Given:
[tex]\begin{gathered} f(x)=x^3-4x+2 \\ g(x)=x^2-6 \end{gathered}[/tex]To solve the problem, we will follow the steps below:
Step 1
Express (f x g)(x)
That is;
[tex](f\times g)(x)=f(x)\times g(x)[/tex]Step 2
Substitute the function into the above.
[tex]=(x^3-4x+2)(x^2-6)[/tex]Step 3
Open the parenthesis.
[tex]=x^2(x^3-4x+2)-6(x^3-4x+2)[/tex][tex]=x^5-4x^3+2x^2-6x^3+24x-12[/tex]Step 4
Re-arrange and simplify.
[tex]=x^5-4x^3-6x^3+2x^2+24x-12[/tex][tex]=x^5-10x^3+2x^2+24x-12[/tex]Therefore,
[tex](f\times g)(x)=x^5-10x^3+2x^2+24x-12[/tex]