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Inverse f(x)

  1. Jan 19, 2010 #1

    Monocerotis

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    Gold Member

    1. The problem statement, all variables and given/known data

    Find the inverse of each function. Is the inverse a function or a relation ?

    f(x) = (x-4)/3



    3. The attempt at a solution
    Not sure which one is correct, and if any are not sure why (as in rules that may apply)

    f(x) = (x-4)/3
    f^-1(x) = 3x+4

    or

    f^-1 3x+12
     
  2. jcsd
  3. Jan 19, 2010 #2
    A way I usually approach such questions is by letting y = f(x), then making x the subject. Clearly then, the expression (in y) will give the inverse function.

    Another way would be by observing that
    [tex]f^{-1} (\frac{x - 4}{3}) = x = (\frac{x - 4}{3}) (3) + 4[/tex]

    You can always check the validity of your function by substituting test values.
     
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