Answer: [tex]x^{6}[/tex] + [tex]6x^{4}[/tex] + [tex]8x^{2}[/tex] + 2
Step-by-step explanation:
f(x) = [tex]x^{3}[/tex] - 4x + 2
g(x) = [tex]x^{2}[/tex] + 2
To find fg(x) , we have
fg(x) = f( [tex]x^{2}[/tex] + 2 )
The next thing is that , we will substitute [tex]x^{2}[/tex] + 2 for the value of x in f(x) , so we have:
[tex](x^{2}+2) ^{3}[/tex] - 4( [tex]x^{2}[/tex] + 2) + 2
which will give
[tex]x^{6}[/tex] + [tex]6x^{4}[/tex] + [tex]8x^{2}[/tex] + 2
Therefore :
fg(x) = [tex]x^{6}[/tex] + [tex]6x^{4}[/tex] + [tex]8x^{2}[/tex] + 2
