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Math Help - Inverse of a Function

  1. #1
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    Inverse of a Function

    Would the inverse of

    f(x)= (x+1)^3

    be

    y = + (the square root of x) - 1

    or

    y= y = - (the square root of x) - 1


    thanks
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  2. #2
    Super Member
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    Jun 2008
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    f(x)= (x+1)^3

    y = (x+1)^3

    Switch y and x:

    x = (y+1)^3

    Solve for y. Take the cube root both sides:

    \sqrt[3]{x} = y+1

    y = \sqrt[3]{x} - 1

    It's neither. If you made a mistake and you actually meant cube root of x instead of square root of x, then the first one is the one.
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  3. #3
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    I did mean the cube root, I'm sorry. I was talking on the phone to my friend about a different problem, ironically, so I messed up. so there's no +/-, it's only plus?

    thanks
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  4. #4
    Super Member
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    Consider this equation: x^n = a

    Case 1:
    If n is even and a>0, then there are two roots: x = \pm\sqrt[n]{a}

    Case 2:
    If n is odd, then there is one root, and it depends on whether a is positive or negative. If b is positive, then x = +\sqrt[n]{b}. Otherwise, if b is negative, then x = -\sqrt[n]{b}
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