2nd Iberoamerican 1987 Problem A1 Find f(x) such that f(x) 2 f( (1-x)/(1+x) ) = 64x for x not 0, ±1.
Put x = (1-y)/(1+y), then (1--x)/(1+x) = y, so f( (1-y)/(1+y) ) 2 f(y) = 64(1-y)/(1+y). Hence f( (1-x)/(1+x) ) 2 f(x) = 64(1-x)/(1+x). But f(x) 4 f( (1-x)/(1+x) ) 2 = 64 2 x 2 , so f(x) 3 = 64 x 2 (1 + x)/(1 - x). Hence f(x) = 4 ( x 2 (1 + x)/(1 - x) ) 1/3 . 2nd Ibero 1987 © John Scholes jscholes@kalva.demon.co.uk 1 July 2002