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# Analysis - functions and continuity watch

1. I'm trying to answer the following question:

Find 5 different functions f: R -> R such that (f(x))2 = x2

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.

Any ideas?
2. (Original post by Will.Honeyman)
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?
No. f must be defined for all points of its domain (R).

Besides that point, I'm not sure. I can think of one more function (-|x|), but a 5th eludes me!
3. There isn't a need for five continuous finctions - just any discontinuos function will do [so x if x is rational -x if x is irrational].

As to the justification still working on that myself.

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Updated: February 1, 2010
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