Question

How do you determine whether the function `f(x)=sqrt(x-2)` has an inverse and if it does, how do you find the inverse function?

Answer 1

`f(x)=sqrt(x-2)` has an inverse, namely `barf(x)=x^2+2`

Explanation:

If `f(x)=sqrt(x-2)`
then
`color(white)("XXX")f^2(x)=x-2`
and
`color(white)("XXX")x=f^2(x)+2`