Question

Please help and show work

Answer 1

28

Explanation:

Given:
`$ g(x) = x^2 + 3 $` and
`$ h(x) = x - 2 $`.

To find the composition of the functions:
`$ (g \circ  h)(x) = g(h(x)) $`

Here,
`$ g(h(x)) = g(x - 2) $`

`$ \implies (x - 2)^2 + 3 $`

`$ \implies x^2 -4x + 4 + 3 = x^2 - 4x +7 $`

We are to find
`$ g(h(7)) $`. That is to substitute
`$ 7 $` in the place of
`$ x $`.

We get:
`$ (7)^2 -4(7) + 7 = 49 - 28 + 7 = 28 $`