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Math Help - Inverse function

  1. #1
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    Inverse function

    The problem says; find and verify the inverse function of f(x)=2x^3 - 4

    I'm stuck on what to do first Any help would be appreciated!
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  2. #2
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    Let y = f^{-1}(x). Then switch the positions of x and f(x) and change f(x) to y (since doing this switch changes f(x)).

    x = 2y^{3} - 4

    Solve for y (i.e. f^{-1}(x)) in terms of x
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  3. #3
    MHF Contributor arbolis's Avatar
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    find and verify the inverse function of f(x)=2x^3 - 4
    Okay. You know that f(f^{-1}(x))=y.
    The idea to find the inverse function of f, that is f^{-1}, is to get x in terms of y. Let y=f(x), then we have y=2x^3-4. Add 4 in each sides of the equation, we get y+4=2x^3. Divide by 2 now, you get \frac{y+4}{2}=x^3. Now take the 3rd root in each sides. You get finally that (\frac{y+4}{2})^\frac{1}{3}=x, or x=(\frac{y}{2}+2)^\frac{1}{3}.
    To verify it, just replace the x you had in your first equation by (\frac{y}{2}+2)^\frac{1}{3} and if you find that it's equal to y, that means you did it.
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