Question

Given that g(x)=x+3 and h(x)=x sqared calculate g-1(7)

Answer 1

In this case, we know
`g(x) = x + 3`, and we are trying to find
`g^(-1)(7)`.

So, we will need to find
`g^(-1)(x)`. Let's do that now:

`y = x + 3`

• Replace
  `g(x)` with
  `y`. This is just simple substitution, nothing major has happened yet.

`x = y + 3`

• Switch
  `x` and
  `y`. This is simply part of the process of finding the inverse function

`y = x - 3`

• Solve for
  `y`

`g^(-1)(x) = x - 3`

• Replace
  `y` with the notation for the inverse function

Now, we are going to solve for when
`x = 7`. To do this, simply "plug in" 7 for
`x` in the inverse function.

`g^(-1)(7) = 7 - 3 = \boxed{4}`

Our answer is 4.