Question

Can a reciprocal function be one-to-one?
if f(x) = 6/ (x-6) was my formula, what is it's inverse?

Answer 1

well swap x and y

start with

\[x = \frac{6}{y -6}\]

and make y the subject...

what changes is the domain...

in some cases the domain is restricted so that inverse is 1 - to - 1. This occurs in inverse of trig functions.

Answer 2

as for reciprocals...

the restrictions in the domain may change..

using your example... the domain restriction is that x cannot equal 6.

take the reciprocal and you get (x -6)/6 domain is all real x.