How do you find the inverse of $f(x)=(2x-3)/(x+1)$ ?

Question

14514 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-06T15:52:27

$f^-1(x)=-(x+3)/(x-2)$

Write as: $y=(2x-3)/(x+1)$

Switch $x$ and $y$ and then solve for $y$ .

$x=(2y-3)/(y+1)$

$x(y+1)=2y-3$

$xy+x=2y-3$

$xy-2y=-x-3$

$y(x-2)=-(x+3)$

$y=-(x+3)/(x-2)$

The $y$ can be replaced by $f^-1(x)$ , which simply denotes an inverse function:

$f^-1(x)=-(x+3)/(x-2)$

How do you find the inverse of f(x)=(2x-3)/(x+1)f(x)=(2x-3)/(x+1)?