Question

G(n)=-2n-2
h (n)=4n-2
Find (goh) (-3)

Answer 1

`(g \circ h)(-3)` = 26

Explanation:

We are told that:

•
`g(n) = -2n - 2`

•
`h(n) = 4n - 2`

In order to calculate the value of
`(g \circ h)(-3)`, we need to first define
`(g \circ h)`.

`(g \circ h)` means that the input for the function
`g(n)` is the function
`h(n)`. Therefore, we have to replace the
`n` in the definition of
`g(n)` with the definition of
`h(n)`:

`(g \circ h)` =
`-2(4n - 2) - 2`

=
`-8n + 4 - 2`

=
`-8n + 2`

Now that we know the definition of
`(g \circ h)`, we can find the value of
`(g \circ h)(-3)` by substituting -3 into the definition:

`(g \circ h)(-3)` =
`-8(-3) + 2`

=
`24 + 2`

=
`26`