RU-ALLRUSSIAN 1987 Problem 20

If the graph of the function $\mathrm{f} = \mathrm{f}(\mathrm{x})$ is rotated through 90 degrees about the origin, then it is not changed. Show that there is a unique solution to $\mathrm{f}(\mathrm{b}) = \mathrm{b}$ . Give an example of such a function.