Question

How do you find the inverse of `f(x)=x^2-6x`?

Answer 1

`f^-1(x)= sqrt(x+9)+3`

Explanation:

First you equate `f(x)` to another variable, say `f(x)=y`.

But before that, complete the square for `f(x)`.

`:. x^2-6x+3^2-3^2=(x-3)^2-9`

Now,
`y=(x-3)^2-9`
`(x-3)^2=y+9`
`(x-3)=sqrt(y+9)`
`x=sqrt(y+9)+3`

Now swap back the x for the variable y.

So the inverse for `f(x)` is
`f^-1(x)= sqrt(x+9)+3`