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

Find 5 different functions f: R -> R such that (f(x))^{2}= x^{2}

How many continuous functions satisfy the requirement? Justify your answer.

2. Relevant equations

3. The attempt at a solution

So far I have:

f(x) = x

f(x) = -x

f(x) = |x|

Could I also have, for example, f(x) = (x^{2}- 5x)/(x-5) as this cancels down to f(x)= x but is undefined at 5?

And I'm not sure how to answer the continuity part, so far all of the functions I have found are continuous (I think?). However, not all continuous functions satisfy it.

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# Homework Help: Functions and continuity

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