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Math Help - Find the Inverse of Fifth Root Function

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    Find the Inverse of Fifth Root Function

    Find the inverse of 5throot of (x^5 + x^4).
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    Re: Find the Inverse of Fifth Root Function

    First of all, is the function one to one?
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    Re: Find the Inverse of Fifth Root Function

    I did not graph the function. Thus, I do not know if it passes the horizontal line test.
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    Re: Find the Inverse of Fifth Root Function

    Not much point in asking for the "inverse function" if you do not know if there is an inverse!

    Perhaps you meant f(x)= \sqrt[5]{x^5+ x^4} with a restricted domain such as x\ge 0?
    Last edited by HallsofIvy; November 2nd 2013 at 07:59 AM.
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    Re: Find the Inverse of Fifth Root Function

    The book's question is find the inverse of the fifth root function as you listed.
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    Re: Find the Inverse of Fifth Root Function

    As who listed? If it just said "find the inverse of the fifth root function", I would interpret that as "find the inverse of [tex]f(x)= x^{1/5}[tex] which is [tex]f^{-1}(x)= x^5[tex].

    If it was "find the inverse function of the function ' \f(x)= \sqrt[5]{x^5+ x^4} for x\ge 0, Then would start by writing x= (y^5+ y^4)^{1/2} then solve for y: x^5= y^5+ y^5 so y^5+ y^4- x^5= 0. Now, unfortunately, there is no simple "fifth degree equation formula" so there is no reasonable formula for solving that equation.
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    Re: Find the Inverse of Fifth Root Function

    Ok. This precalculus textbook has many questions in the "Challenge" section at the end of each chapter. Personally, my answer would be: Question is too complex for this level of math. I would much rather find the inverse of functions like y = x^2 + 3 or
    y = 1/(x+4) than to deal with fifth root functions.
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