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Math Help - inverse function

  1. #1
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    inverse function

    1>what is the value of d/dx(f^-1 (x)) when x=2 and f(x)=x^3+x and f^-1(2)=1
    (a) 1/13 (b) 1/4 (c) 1/2 (d)7/4

    2>Inverse of f(x)= cuberoot((1+x)/2x)
    (a)(2x/(1+x))^3
    (b) 1/(2x^3-1)
    (c)(1/(2x-x))^3
    (d)2x/(x^3-1)
    Last edited by gracy; February 5th 2007 at 12:37 AM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by gracy View Post
    2>Inverse of f(x)= cuberoot((1+x)/2x)
    (a)(2x/(1+x))^3
    (b) 1/(2x^3-1)
    (c)(1/(2x-x))^3
    (d)2x/(x^3-1)
    Here's how to find an inverse:
    Given the function y = f(x), switch the roles of x and y. Thus you have the equation x = f(y). Now solve for y and that gives you your inverse function.

    Example:
    f(x) = \sqrt[3]{\frac{1+x}{2x}}

    Set y = f(x) = \sqrt[3]{\frac{1+x}{2x}}

    Now switch the x and y:
    x = \sqrt[3]{\frac{1+y}{2y}}

    Now solve for y:
    x^3 = \frac{1+y}{2y}

    2yx^3 = 1+y

    2yx^3 - y = 1

    y(2x^3 - 1) = 1

    y = \frac{1}{2x^3 - 1}

    Thus:
    f^{-1}(x) = \frac{1}{2x^3 - 1}

    -Dan
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