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Math Help - Function Properties Not Inherited By Inverses

  1. #1
    Member Rimas's Avatar
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    Function Properties Not Inherited By Inverses

    Suppose that f has an inverse function f^(-1).For Each Of the Following Properties Give an example to show that f can have the property while its inverse does not

    [a] f has a graph with a horizontal asymptote
    [b] f has a domain all real numbers
    [c] f has a graph that is bounded above
    [d] f has a removable discontinuity at x=5
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Rimas View Post
    Suppose that f has an inverse function f^(-1).For Each Of the Following Properties Give an example to show that f can have the property while its inverse does not

    [a] f has a graph with a horizontal asymptote
    f(x) = e^x

    [b] f has a domain all real numbers
    f(x) = x^2

    [c] f has a graph that is bounded above
    f(x) = -x^2

    [c] f has a removable discontinuity at x = 5
    f(x) = \left \{ \begin{array}{lr} x - 5 & \mbox{ if } x \ne 5 \\ x & \mbox{ if } x = 5 \end{array}\right.
    Last edited by Jhevon; October 13th 2007 at 08:20 PM.
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