# How do you find the inverse of f(x) = 4 / (x+2)?

May 8, 2017

Replace the original x with y and original y with x and solve for y.

#### Explanation:

We can find the inverse of any function by replacing the original function's x with y and y with x and solving.
For this function, $f \left(x\right)$ is the same as y, so we can write this function as:
$y = \frac{4}{x + 2}$
Now we flip the x and the y to get:
$x = \frac{4}{y + 2}$
Now we solve for the new y:
$x \left(y + 2\right) = 4$
$y + 2 = \frac{4}{x}$
$y = \frac{4}{x} - 2$
So our inverse function is: ${f}^{- 1} \left(x\right) = \frac{4}{x} - 2$