Question

Find (g∘g)(−1)for g(x)=4x2+3x−3. (g∘g)(−1)=

Answer 1

Given:

`g(x)=4x^2+3x-3`

We're asked to find the value of:

`(g\circ g)(-1)`

What we're going to do is to find the value of g(-1) first:

`(g\circ g)(-1)=g(g(-1))`
`\begin{gathered} g(-1)=4(-1)^2+3(-1)-3 \\ g(-1)=4-3-3 \\ g(-1)=-2 \end{gathered}`

Now,

`g(g(-1))=g(-2)`

The value of the composite function equals g(-2):

`\begin{gathered} g(-2)=4(-2)^2+3(-2)-3 \\ g(-2)=4(4)-6-3 \\ g(-2)=16-6-3 \\ g(-2)=7 \end{gathered}`

Therefore,

`(g\circ g)(-1)=7`