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F(f^-1) = x

  1. Feb 7, 2006 #1
    can anybody pls give me an example of this f(f^-1) = x??
  2. jcsd
  3. Feb 7, 2006 #2
    It's the definition of the inverse of a function f(x). For example, y = 2x and y^-1 = 1/2 x
  4. Feb 7, 2006 #3
    how about if i want to write it using sin x??
  5. Feb 7, 2006 #4


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    Although I would say f(f-1(x))= x. You're missing the "x" on the left side!

    "arcsine" is defined as the inverse of sine (that's why your calculator has them paired). sin(arcsin(x))= x.

    There are "technical" problems. Since sin(x) is not "one-to-one" ([itex]sin(\pi)= 0= sin(0)[/itex]) there can't be a true inverse (a function can't return both 0 and [itex]\pi[/itex] for x= 0). What is normally done is restrict the sine function to x=0 to [itex]\pi[/itex] (which is really a different function than sine defined for all x) so that arcsin returns the "principal value"- the value between 0 and [itex]\pi[/itex].
  6. Feb 8, 2006 #5


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    We don't really restrict sin function to x = 0 to [itex]\pi[/itex].
    We, however, restrict sin function to [tex]x = -\frac{\pi}{2}[/tex] to [tex]x = \frac{\pi}{2}[/tex]. :)
  7. Feb 8, 2006 #6


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    Oops! It's cosine that is restricted to "between 0 and [itex]\pi[/itex]!
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