# Math Help - Inverse of a function

1. ## Inverse of a function

Find the inverse of f(x)= x/(x+1)

I have no idea where to begin. Everything I've tried just takes me back to the original problem.

2. $y = \frac{x}{x+1}$

Swap x and y and slove for y

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

$x(y+1) =y$

$xy +x -y = 0$

$xy -y = -x$

$y(x-1) = -x$

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

3. Originally Posted by The Box
Find the inverse of f(x)= x/(x+1)

I have no idea where to begin. Everything I've tried just takes me back to the original problem.
$f\left( x \right) = \frac{x}
{{x + 1}} \hfill \\$

${\text{Let, }}y = \frac{x}
{{x + 1}} \hfill \\$

${\text{For finding inverse, interchange }}x{\text{ and }}y{\text{, and solve for y}} \hfill \\$

$\Rightarrow x = \frac{y}
{{y + 1}} \hfill \\$

$\Rightarrow x\left( {y + 1} \right) = y \hfill \\$

$\Rightarrow xy + x = y \hfill \\$

$\Rightarrow x = y - xy \hfill \\$

$\Rightarrow x = y\left( {1 - x} \right) \hfill \\$

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

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

${\text{Inverse of }}f\left( x \right){\text{ is }}f^{ - 1} \left( x \right) = \frac{x}
{{1 - x}} \hfill \\$

4. Thank you! I can't believe I never saw bringing y to the left side...