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

Independence of two functions

  1. Sep 14, 2008 #1
    When are to functions y1 = f1(x) and y2 = f2(x) independent? It would apper never, because, we can always write x = f1-1 (y1), and therefore y2 is a function of y1. Every function is dependent of any other function. Generally, dy1/dy2 != 0 for arbitrary functions y1 and y2. Is this reasoning correct?
  2. jcsd
  3. Sep 14, 2008 #2

    Ben Niehoff

    User Avatar
    Science Advisor
    Gold Member

    We can, however, talk about linearly-independent functions: namely, functions with vanishing Wronskian.
  4. Sep 14, 2008 #3


    User Avatar
    Homework Helper

    I can't figure out what the OP is saying about independent functions. It's not the same as the concept of linear independence, is it?
  5. Sep 14, 2008 #4


    User Avatar
    Homework Helper

    It's when the Wronskian doesn't vanish that the two functions are linearly independent.
  6. Sep 15, 2008 #5


    User Avatar
    Staff Emeritus
    Science Advisor

    I have no idea what you are saying! Do y1, y2, x1, x2 just represent numbers? What, then, is the difference between saying y1= f1(x1) and just y= f1(x)? And, of course, what do you mean by "independent"? Apparently you don't mean "linear independence". Before anyone can tell you whether or not "any two functions are not independent" you will have to say what you mean by two functions being "independent"!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Independence of two functions