Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding unknown functions

  1. Sep 16, 2004 #1
    Say you get a problem like this:
    Find f(x) and g(x) when f(g(x))=|sin(x)| and g(f(x))=sin^2(sqrt(x)),
    and Domain_f=R, Domain_g=[0,-> >

    How would you approach to solve this, or do you have to keep guessing until you find two functions that fits?
     
  2. jcsd
  3. Sep 16, 2004 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    You'll have to keep guessing until you see:
    f(x)=sqrt(x)
    g(x)=sin^2(x)
    Are you sure about the domains?
     
  4. Sep 16, 2004 #3
    I was looking for an algorithm or something that would work, when the example wasnt as simple as this one. When alot of simplifying had been done to the expressions for example.

    And of course, the domains are reversed. Sorry about that.
     
  5. Sep 16, 2004 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    No, there are no general solve-all techniques for functional equations
    (where your unknowns are functions, rather than some numbers, for example)
     
  6. Sep 16, 2004 #5
    Of course mathematicians don't want to be perceived as just guessing at possible answers so they have termed this method "solution by inspection." :biggrin:
     
  7. Sep 16, 2004 #6

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    :biggrin::biggrin::biggrin::biggrin::biggrin:
     
  8. Sep 16, 2004 #7

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    Hey, trial and error is a perfectly valid mathematical method! Of course it's not always the most efficient path to a solution. :-)
     
  9. Sep 17, 2004 #8

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Well, it's a perfectly valid praxis, don't know about method though..:wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?