# How do you find the inverse function of the function f(x) = 3/x?

Jul 13, 2017

${f}^{-} 1 \left(x\right) = \frac{3}{x}$

#### Explanation:

$f \left(x\right) = \frac{3}{x}$
$y = \frac{3}{x}$

Switch the variables, and solve for $y$.

$x = \frac{3}{y}$
$x y = 3$
$y = \frac{3}{x}$

${f}^{-} 1 \left(x\right) = \frac{3}{x}$

So, the inverse of $f \left(x\right) = \frac{3}{x}$ is itself.