Question

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

(QUESTION3.11)

Answer 1

Answer:
`x^(6)` +
`6x^(4)` +
`8x^(2)` + 2

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