Question

F(x)=x^2-2 and g(x)=x^3+2(f•g)(-2)=

Answer 1

Given the functions:

`\begin{gathered} f\mleft(x\mright)=x^2-2 \\ \\ g\mleft(x\mright)=x^3+2 \end{gathered}`

You need to multiply them in order to find:

`(f\cdot g)(x)`

Then, you get:

`(f\cdot g)(x)=\mleft(x^2-2\mright)\mleft(x^3+2\mright)`
`(f\cdot g)(x)=(x^2)(x^3)+(x^2)(2)-(2)(x^3)-(2)(2)^{}`
`(f\cdot g)(x)=x^5+2x^2-2x^3-4`
`(f\cdot g)(x)=x^5-2x^3+2x^2-4`

Substitute the following value of "x" into the function:

`x=-2`

And then evaluate, in order to find:

`\mleft(f\cdot g\mright)\mleft(-2\mright)`

Then, you get:

`(f\cdot g)(-2)=(-2)^5-2(-2)^3+2(-2)^2-4`
`\begin{gathered} (f\cdot g)(-2)=(-2)^5-2(-2)^3+2(-2)^2-4 \\ \\ (f\cdot g)(-2)=-32-2(-8)^{}+2(4)^{}-4 \end{gathered}`
`(f\cdot g)(-2)=-32+16^{}+8^{}-4`
`(f\cdot g)(-2)=-12`

Hence, the answer is:

`(f\cdot g)(-2)=-12`