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

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Answer 1 · 2015-09-16T07:07:23

$f^-1(x)$ = $(x-1)/(x-2)$

let $f_x$ = $y$
$x=f^-1y$
$y$ = $(2x-1)/(x-1)$

$y$ = $1$ + $x/(x-1)$

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

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

$-1/x$ = $1/(y-1)-1$
$x=(y-1)/(y-2)$
$f^-1y$ = $(y-1)/(y-2)$
replacing y with x
$f^-1(x)$ = $(x-1)/(x-2)$

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