Question

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

Answer 1

If `h(x)` is the inverse of `g(x)`
then `h(x) = (x^2+72)/9`

Explanation:

Note that if `h(x)` is the inverse of `g(x)`
`color(white)("XXX")g(h(x))=x`
and
substituting `h(x)` for `x` in the original definition of `g(x)`
`color(white)("XXX")g(h(x)) = 3sqrt(h(x)-8)`

Therefore
`color(white)("XXX")3sqrt(h(x)-8)=x`

`color(white)("XXX")sqrt(h(x)-8) = x/3`

`color(white)("XXX")h(x)-8 = x^2/9`

`color(white)("XXX")h(x) = (x^2+72)/9`