The binverse/b of a function is one that performs the opposite operation to the original function. Inverse functions only exist for one-to-one functions.

The inverse of the function (f(x)) is (f^-1(x)).

When a function is put into its inverse function, or when an inverse function is put into its function, the result is always (x):

(ff^-1(x) = f^{-1}f(x) = x)

uDomain and range/u

The bdomain/b of a function is the brange/b of its inverse function. The brange/b of a function is the bdomain/b of its inverse function.

uGraphical relationship/u

On a graph, an inverse function is the reflection of its function about the (y=x) line.

For example, (f(x)) is represented by the purple line, (f^-1(x)) the green line and (y=x) the red dashed line.

mtaimg/images/topics/2/2-21-1.png/mtaimg

(ff^-1(x) = f^{-1}f(x) = x)

The bdomain/b of a function is the brange/b of its inverse function. The brange/b of a function is the bdomain/b of its inverse function.

On a graph, an inverse function is the reflection of its function about the (y=x) line.