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Math Help - Finding the Inverse of a Funtion

  1. #1
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    Finding the Inverse of a Funtion



    How would I go about solving this?
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  2. #2
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    First make it a "Y=" equation.

    Y = x2-5x+6

    Switch the Y with the x's

    X = Y2-5Y+6

    Solve for X

    X-6 = Y2-5Y

    X-6/5 = Y2

    Square root of ((x-6)/5)) = Y

    Kind of confusing, but I hope this helps!
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  3. #3
    Senior Member euclid2's Avatar
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    Quote Originally Posted by Aske View Post


    How would I go about solving this?
    The easiest way to go abouts doing this is making a table of values for the function and switching the values of the y and x. what i mean is make the x values the y values and the y values the x values. This will give you the inverse, f-1(x)
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  4. #4
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    Quote Originally Posted by Aske View Post


    How would I go about solving this?
    You don't. That is not a "one to one" function and so does not have an inverse. If f^{-1}(x) is the inverse of f(x), then we must have f^{-1}(f(x))= x, that is, f^{-1} must 'undo' whatever f does. But f(6)= 0 and f(-1)= 0. f^{-1}(0) can't be both 6 and -1!

    Luke774, for some reason, chose to take only the "+" sign on the square root. That's valid but gives the inverse of a slightly different function: f(x)= x^2- 5x- 6 with x\ge 5/2 and undefined for x< 5/2. Same formula but different domain so different function.
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