# How do you find the inverse of f(x) = (2x-1)/(x-1)?

Sep 16, 2015

${f}^{-} 1 \left(x\right)$= $\frac{x - 1}{x - 2}$

#### Explanation:

let ${f}_{x}$ = $y$
$x = {f}^{-} 1 y$
$y$ = $\frac{2 x - 1}{x - 1}$

$y$ = $1$+$\frac{x}{x - 1}$

$y - 1$=$\frac{x}{x - 1}$

$\frac{1}{y - 1}$=$1 - \frac{1}{x}$

$- \frac{1}{x}$=$\frac{1}{y - 1} - 1$
$x = \frac{y - 1}{y - 2}$
${f}^{-} 1 y$= $\frac{y - 1}{y - 2}$
replacing y with x
${f}^{-} 1 \left(x\right)$= $\frac{x - 1}{x - 2}$