Question

Let f(x)=x2-2 and g(x)=9-X. Perform the composition or operation indicated.(fg)(-7)

Answer 1

Given the functions below

`\begin{gathered} f(x)=x^2-2 \\ g(x)=9-x \end{gathered}`

We are to find (fg)(-x)

SOLUTION

First of all, we have to get (fg)(x)

`(fg)(x)=(x^2-2)(9-x)`

Expand the function

`\begin{gathered} (fg)(x)=x^2(9-x)-2(9-x) \\ (fg)(x)=9x^2-x^3-18+2x \\ \therefore(fg)(x)=-x^3+9x^2+2x-18 \end{gathered}`

Let us now solve for (fg)(-7)

`\begin{gathered} (fg)(-7)=-(-7)^3+9(-7)^2+2(-7)-18 \\ (fg)(-7)=343+441-14-18=752 \end{gathered}`

Hence,

`(fg)(-7)=752`