Question

What is (f⋅g)(x)? f(x)=x3−4x+2 g(x)=x2+2 Enter your answer in the box. (f⋅g)(x)=

Answer 1

Answer: $x^{6}$ + $6x^{4}$ + $8x^{2}$ + 2

Step-by-step explanation:

f(x) = $x^{3}$ - 4x + 2

g(x) = $x^{2}$ + 2

To find fg(x) , we have

fg(x) = f( $x^{2}$ + 2 )

The next thing is that , we will substitute  $x^{2}$ + 2 for the value of x in f(x) , so we have:

$(x^{2}+2) ^{3}$ - 4( $x^{2}$ + 2) + 2

which will give

$x^{6}$ + $6x^{4}$ + $8x^{2}$ + 2

Therefore :

fg(x) = $x^{6}$ + $6x^{4}$ + $8x^{2}$ + 2