Question

What is the inverse function of `f(x)=3+sqrt(x-8)`?

Answer 1

(Because I find it easier to work with, I am replacing `f(x)` with `y`

Given `y = 3+sqrt(x-8)`

We want to write an equivalent relationship of the form
`x =` and expression in terms of `y`

`y = 3+sqrt(x-8)`

`sqrt(x-8) = y-3`

`x-8 = y^2-6y+9`

`x = y^2 -6y +17`

It is possible to verify that this is the inverse of the given equation by plugging `3+sqrt(x-8)` into `x=y^2-6y+17` in place of `y`.
The result (after simplifying) will be `x=x`