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Continuous Functions

  1. Jun 14, 2013 #1
    1. The problem statement, all variables and given/known data
    How many continuous functions f are there which satisfy the equation (f(x)^2) = x^2 for all x?


    2. Relevant equations



    3. The attempt at a solution
    What method should I use to solve this? Is there a specific strategy involved besides plug and chug? Off the top of my head, I can only think of f(x)= x, but that's just one. Thank you.
     
  2. jcsd
  3. Jun 14, 2013 #2

    Office_Shredder

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    If you take square roots:
    [tex] \sqrt{ a^2} = |a| [/tex]
    Is always a true statement regardless of whether a is positive or negative. So for your equation you get |f(x)| = |x|. Try working from there
     
  4. Jun 14, 2013 #3
    Thank you so much for that derivation!
    For this absolute function, there would be two possible values: -x and x.
    There would only be two functions possible then I think?
    I thought it would be more complicated, and involve log functions, etc.
     
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