How do you find $f ^-1(x)$ given $f(x) = (x+1)/(x+2)$ when x ≠ -2?

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Answer 1 · 2016-06-15T10:34:48

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

First : we will replace all $x$ by $y$ and the $y$ by $x$

Here we have :
$x=(y+1)/(y+2)$

Second: solve for $y$

$x*(y+2)=y+1$
$x*y +2*x = y+1$

Arrange all $y$ in one side:

$x*y - y= 1-2*x$

Taking $y$ as common factor we have:
$y*(x-1)=1-2*x$
$y=(1-2*x)/(x-1)$

Therefore,
$f^-1(x)=(1-2*x)/(x-1)$

How do you find f ^-1(x)f ^-1(x) given f(x) = (x+1)/(x+2)f(x) = (x+1)/(x+2) when x ≠ -2?