1. The problem statement, all variables and given/known data A function f(x) is continuous in the range [-1,1] f(x) = 2xf(x2 - 1) Prove that f(x) = 0 everywhere in range [-1,1] 2. Relevant equations I don't know how to proceed. By putting values as x = 0, I got f(0) = 2*0 = 0. f(1) = 2*1*f(0) = 0. And I also get f(negative values) = f(positive values). So it's like a cosine wave. But how to prove that the values are equal to zero. 3. The attempt at a solution How to proceed? Continuous means value of f(x) when I approach from left side = value of f(x) when I approach from right side. Not sure how to imply it here.