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]
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.
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.