# What is the inverse of the function f(x) = 2x + 1?

Feb 20, 2018

$y = 0.5 \left(x - 1\right)$

#### Explanation:

To find the inverse of a function, you have to substitute $y$ for $x$ in the equation and simplify to get a normal equation again. In this case, $f \left(x\right)$ is $y$.

$y = 2 x + 1$

$x = 2 y + 1$

$2 y + 1 = x$

$2 y = x - 1$

$y = 0.5 \left(x - 1\right)$

So there you have it.

Feb 20, 2018

${f}^{- 1} \left(x\right) = \frac{x - 1}{2}$

#### Explanation:

$f \left(x\right) = y$

$y = 2 x + 1$

Switch the places of x and y:

$x = 2 y + 1$

Now, solve for y so the function is once again written in terms of x:

$2 y = x - 1$

$y = \frac{x - 1}{2}$

${f}^{- 1} \left(x\right) = \frac{x - 1}{2}$

Where ${f}^{- 1} \left(x\right)$ denotes that the function is an inverse of the original function.