Precalculus · Problem 20

Further Topics in Functions — Stitz & Zeager

Mathematics — Precalculus · inverse-functions

Problem

Show that

f(x) = \dfrac{x-2}{2x-1}

is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of

f

is the domain of

f^{-1}

and vice-versa.