Inverse of $$$y = \ln\left(x\right)$$$

The calculator will try to find the inverse of the function $$$y = \ln\left(x\right)$$$, 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: $$$y = \ln\left(x\right)$$$ becomes $$$x = \ln\left(y\right)$$$.

Now, solve the equation $$$x = \ln\left(y\right)$$$ for $$$y$$$.

$$$y = e^{x}$$$

Answer

$$$y = e^{x}$$$A

Graph: see the graphing calculator.