460

Part of 1987 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 460 All Soviet Union MO 1987 rotate plot of a function, f(x)=x

Source:

The plot of the

y=f(x)

function, being rotated by the (right) angle around the

(0,0)

point is not changed.
a) Prove that the equation

f(x)=x

has the unique solution.
b) Give an example of such a function.

rotationfunctionplotequation