(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.

**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!

# Functions and continuity

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