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Question about inverse functions

  1. Jul 31, 2008 #1
    If you've already found that F(g(X))=X, is it necessarry to also prove that g(f(X))=X to know that you have inverse functions? Would there be a case where the first statement is true but the second is false?
     
  2. jcsd
  3. Jul 31, 2008 #2
    The inverse of many functions are not functions themselves.
     
  4. Jul 31, 2008 #3

    HallsofIvy

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    In particular, if [itex]f(x)= x^2[/itex]] and [itex]g(x)= \sqrt{x}[/itex], [itex]f(g(x))= (\sqrt(x))^2= x[/itex] but [itex]g(f(x))= \sqrt{x^2}= |x|[/itex]. Of course, if the domain of f is restricted to the non-negative numbers, then they are inverses.
     
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