Question

Given f(x) = x squared - 1 and g(x) = x+ 2, what is the value of h(-2) where h(x) = f(g(x))?

Answer 1

Answer:
`h(-2)=-1`

Explanation:

We need to find
`f(g(x))`. Substitute the function
`g(x)` into the function
`f(x)`:

`f(g(x)) = (x+ 2)^2- 1`

Now, we know that the function
`h(x)` is
`h(x)=f(g(x))`, then:

`h(x)=(x+ 2)^2- 1`

In order to find the value of
`h(-2)`, we must substitute
`x=-2` into the function
`h(x)=(x+ 2)^2- 1`.

Therefore, the value of
`h(-2)` is:

`h(x)=(x+ 2)^2- 1\\\\h(-2)=(-2+ 2)^2- 1\\\\h(-2)=(0)^2- 1\\\\h(-2)=0-1\\\\h(-2)=-1`