We've only been taught of limits and derivatives and integration. I tried using derivatives. f(x) = 2x(f(x2-a)) Let f(x^2 - 1) = g(x) So f(x) = 2x g(x) f'(x) = 2xg'(x) + 2g(x) f'(x) = 2xf'(x)(2x) + 2f(x^2 - 1) f'(x) (1-4x^2) = 2f(x^2 - 1) So we get f'(x) = 2f(x^2 - 1)/(1-4x^2) Now we got that f(-1) = f(1) = 0. So if f(x) is non zero at any point between 1 and -1, then f'(x) must be positive some place and negative some place. But above we see that f'(x) is an even function. So f'(x) is not satisfying condition of positive and negative. It's either positive or negative and if it's one of them then it can have only 1 zero. And so we can say that f(x) is constant at zero. Aren't all continuous functions derivative? I'm not sure what's the difference. Sine and consine are continous and differentiable. So i guess it should be true.