# Inverse of a function

This applet shows the inverse relation of a function.
The inverse of is a relation . Graphically, the inverse relation is obtained by reflecting the graph of about the line .

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 . 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 to make the inverse a function?