MathDB

2

Part of 1983 Canada National Olympiad

Problems(1)

Unchanged functions after transformation

Source: Canadian Mathematical Olympiad - 1983 - Problem 2.

6/26/2011
For each r∈Rr\in\mathbb{R} let TrT_r be the transformation of the plane that takes the point (x,y)(x, y) into the point (2rx;r2rx+2ry)(2^r x; r2^r x+2^r y). Let FF be the family of all such transformations (i.e. F={Tr:r∈R}F = \{T_r : r\in\mathbb{R}\}). Find all curves y=f(x)y = f(x) whose graphs remain unchanged by every transformation in FF.
functionlogarithmsalgebrafunctional equationalgebra unsolved