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Math Help - Algebraically disproving equal functions

  1. #1
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    Algebraically disproving equal functions

    Hey,

    Given the function f(x)=3x-4, show algebraically, that f^-1(x) is NOT equal to f(x).

    Do I solve for the inverse equation to get y=1/3(x+4) and then sub in values for (x) to get different y-values that do not equal each other? How else could I prove this?

    Thanks!
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  2. #2
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    Quote Originally Posted by MATHDUDE2 View Post
    Hey,

    Given the function f(x)=3x-4, show algebraically, that f^-1(x) is NOT equal to f(x).

    Do I solve for the inverse equation to get y=1/3(x+4) and then sub in values for (x) to get different y-values that do not equal each other? How else could I prove this?

    Thanks!
    If f(x) := y = 3x - 4 then f^{-1} := x = 3y - 4

    Some rearranging gives

    3y = x + 4

    y = \frac{1}{3}x + \frac{4}{3}.


    I think it's pretty clear that f(x) \neq f^{-1}(x) for all x.
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