# Functions and continuity

1. Jan 31, 2010

### Kate2010

1. The problem statement, all variables and given/known data
Find 5 different functions f: R -> R such that (f(x))2 = x2

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) = (x2 - 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.

Last edited: Jan 31, 2010
2. Jan 31, 2010

### Staff: Mentor

What does your notation (f(x))2 = x2 mean?

3. Jan 31, 2010

### Kate2010

Oh I'm sorry I typed it incorrectly. I meant squared but did subscript not superscript, it's edited now.

4. Jan 31, 2010

### Staff: Mentor

I think that the fourth function you list satisfies the requirement that (f(x))2 = x2, so it should be easy to get one more.

The first three functions you listed are continuous, but the fourth one isn't, because it isn't continous at x = 5.