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Functions and continuity

  1. Jan 31, 2010 #1
    1. The problem statement, all variables and given/known data
    Find 5 different functions f: R -> R such that (f(x))2 = x2

    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) = (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. jcsd
  3. Jan 31, 2010 #2

    Mark44

    Staff: Mentor

    What does your notation (f(x))2 = x2 mean?
     
  4. Jan 31, 2010 #3
    Oh I'm sorry I typed it incorrectly. I meant squared but did subscript not superscript, it's edited now.
     
  5. Jan 31, 2010 #4

    Mark44

    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.
     
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