(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Prove f(x) is zero in range [-1,1]

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**