# How do you find the inverse of f(x) = \frac{1}{x-5} algebraically?

Oct 24, 2014

Step 1:

$f \left(x\right) = \frac{1}{x - 5}$

Change $f \left(x\right)$ to $y$

$y = \frac{1}{x - 5}$

Step 2:

Switch $x$ and $y$

$x = \frac{1}{y - 5}$

Step 3:

Solve for $y$

$x \left(y - 5\right) = 1$

$\frac{x \left(y - 5\right)}{x} = \frac{1}{x}$

$\left(y - 5\right) = \frac{1}{x}$

$y = \frac{1}{x} + 5$