Question

Given the definitions of f(x) and g(x) below, find the value of f(g(-9))(2) = x2 - 6x - 9g(2) -2x - 14

Answer 1

Given:

The functions are,

`f(x)=x^2-6x-9`
`g(x)=-2x-4`

Step-by-step explanation:

Determine the function for f(g(x)).

`f(g(x))=(-2x-14)^2-6(-2x-14)-9`

Substitute -9 for x in the obtained equation to obtain the value of f(g(-9)).

`\begin{gathered} f(g(-9))=(-2\cdot(-9)-14)^2-6(-2\cdot(-9)-14)-9 \\ =(18-14)^2-6(18-14)-9 \\ =16-24-9 \\ =-17 \end{gathered}`

So value of f(g(-9)) is -17.

Answer: -17