Inverse of $$$y = 2 x + 1$$$

The calculator will try to find the inverse of the function $$$y = 2 x + 1$$$, with steps shown.

Related calculator: Inverse Function Calculator

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: $$$y = 2 x + 1$$$ becomes $$$x = 2 y + 1$$$.

Now, solve the equation $$$x = 2 y + 1$$$ for $$$y$$$.

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

Answer

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

Graph: see the graphing calculator.