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GeoGebraGeoGebra Classroom

Inverse Function


A function converts an value to a value so the inverse operation would take a value back to the original value. Because the inverse operation would take a value to an value the axis and names are switched. The inverse operation of a function can be shown on a graph by reflecting the function about the line which is equivalent to switching the and axes. The inverse of a function is labeled as . However, not all functions have inverse functions. You can enter a function in the entry box. This applet will then tell whether the inverse operation is a function. This test is performed only on the visible portion of the domain of the inverse operation. Checking the "Path" checkbox will show the path of numbers. By moving the initial x value ( the orange plus ) it can be seen that if is a function. Also, from exchange of functions


Determine what requirement must the original function satisfy in order to have an inverse function. Also, note the Domain and Range of the function and inverse operation. Is there a way to limit the domain or range of the flipped function so that it could be a function.