# Inverse of a function

This applet shows the inverse relation of a function.

The inverse of $y = f(x)$ is a relation $x = f^{-1}(y)$. Graphically, the inverse relation is obtained by reflecting the graph of $y = f(x)$ about the line $y=x$.

Enter the rule for a function $f(x)$ in the textbox at bottom-left. Click ‘Show points’ to display a point on the x-axis, and the point(s) corresponding to $f^{-1}(x)$. Drag the blue point to change $x$.

What do you get as you drag x along the axis?

Click ‘Show inverse’ to display the entire inverse relation. Is it a function? You can click ‘Vertical line test’ to provide a vertical line which might help you decide.

Can you restrict the domain of $f$ to make the inverse a function?

Other resources:

Geogebratube page for this applet