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Math Help - Inverse Function

  1. #1
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    Inverse Function

    I am having trouble with this problem:

    Show that, for every value of a, the function

    f(x)= a + (1/(x-a))

    is its own inverse.
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  2. #2
    Senior Member vincisonfire's Avatar
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     y= a + \frac{1}{x-a}
    Switch x and y and solve for y to find inverse
     x= a + \frac{1}{y-a}
     x - a = \frac{1}{y-a}
     y - a = \frac{1}{x-a}
     y = a + \frac{1}{x-a}
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