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Homework Help: Explicit Expression

  1. Jun 30, 2008 #1
    For the function f given by the equation f(x)=[tex]\frac{-2x}{3x-4}[/tex], determine where the relation f^-1 is a function. If f^-1 is a function, write an explicit expression for f^-1(x).

    Need help writing explicit expression. Any guidance?
     
  2. jcsd
  3. Jun 30, 2008 #2
    You have to check if the given function is invertible or not.If it is one-one and onto then it is invertible and f^-1 is a function or it exists.
    I don't get you , when you say 'explicit function'.You mean the inverse?
     
  4. Jun 30, 2008 #3

    HallsofIvy

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    Science Advisor

    You first say "determine where the relation f-1 is a function" which implies that f-1 is a function for some values of x, not others. But then you say "If f-1 is a function". Are you sure it wasn't "determine whether the relation f-1 is a function?

    Let [itex]y= \frac{-2x}{3x-4}[/itex] and "swap" x and y:
    [tex]x= \frac{-2y}{3y-4}[/itex]
    Now can you solve that for y? If so, f-1 exists and you have found it.
     
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