Question

I need help with this question plsss

Answer 1

Answer:

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

Step-by-step 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.

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