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    • Thread Starter

    I'm trying to answer the following question:

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

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

    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?

    (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!

    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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