- #1

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## Homework Statement

A function f(x) is continuous in the range [-1,1]

f(x) = 2xf(x

^{2}- 1)

Prove that f(x) = 0 everywhere in range [-1,1]

## Homework 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.

## 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.