Inverse function (basic algbra math)

Question

Consider the following function: $f(x) = {1 / (x-6) }$

Find a formula for the inverse of the function.

Here is what have so far?

$y = 1/(x-6)$ ---> $ x = 1/(y-6) $

But my embarrassing problem is that I don't remember how to get the variable out of the denominator.

Multiply both sides by $(y-6)$? to get $x(y-6) = 1$?

Answer 1

Continuing from where you left off

x(y-6)=1

y-6=1/x

y=1/x + 6

Answer 2

f = 1/x-6 is Mobius so inverse f = (-6x -1)/-x = 6 + 1/x