Answer:
In standard form, the answer is [tex](f*g)(x)=x^{6}+6x^{4}+8x^{2}+2[/tex].
Step-by-step explanation:
[tex](f*g)(x)[/tex] is the same as saying [tex]f(g(x))[/tex].
Simply put, sub into [tex]f(x)[/tex] using the definition of [tex]g(x)[/tex] as an x-value.
[tex]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[/tex]
