# Inverse Function Calculator

## Find inverse function step by step

The calculator will find the inverse of the given function, with steps shown. If the function is one-to-one, there will be a unique inverse.

### Your Input

**Find the inverse of the function $$$y = \frac{x + 7}{3 x + 5}$$$.**

### Solution

To find the inverse function, swap $$$x$$$ and $$$y$$$., and solve the resulting equation for $$$y$$$.

This means that the inverse is the reflection of the function over the line $$$y = x$$$.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: $$$y = \frac{x + 7}{3 x + 5}$$$ becomes $$$x = \frac{y + 7}{3 y + 5}$$$.

Now, solve the equation $$$x = \frac{y + 7}{3 y + 5}$$$ for $$$y$$$.

$$$y = \frac{7 - 5 x}{3 x - 1}$$$