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Math Help - Inverse of an absolute function

  1. #1
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    Inverse of an absolute function

    Hey guys, just wondering how you would go about determining f^(-1) (x) of the function,

    f(x) = x + |x|/2

    What I did first was that I let f(x) = y. Then, I switched the x and the y variables

    y = x + |x|/2

    x = y + |y|/2

    I don't know how to isolate for y since part of it is in absolute notation. Help?
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  2. #2
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    Re: Inverse of an absolute function

    Math Forum - Ask Dr. Math

    ....googling does wonders...
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  3. #3
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    Re: Inverse of an absolute function

    I still don't understand how I would apply it to the function I described, since it is partly an absolute value function.
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  4. #4
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    Re: Inverse of an absolute function

    Quote Originally Posted by Manni View Post
    Hey guys, just wondering how you would go about determining f^(-1) (x) of the function,
    f(x) = x + |x|/2
    Do you understand that any linear function mx+b has an inverse?

    Do you see that x + \frac{{\left| x \right|}}{2} = \left\{ {\begin{array}{rl}   {\dfrac{{3x}}{2},} & {x \geqslant 0}  \\   {\dfrac{x}{2},} & {x < 0}  \\ \end{array} } \right.
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