# Thread: Find the Inverse of Fifth Root Function

1. ## Find the Inverse of Fifth Root Function

Find the inverse of 5throot of (x^5 + x^4).

2. ## Re: Find the Inverse of Fifth Root Function

First of all, is the function one to one?

3. ## 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.

4. ## 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 $\displaystyle f(x)= \sqrt[5]{x^5+ x^4}$ with a restricted domain such as $\displaystyle x\ge 0$?

5. ## Re: Find the Inverse of Fifth Root Function

The book's question is find the inverse of the fifth root function as you listed.

6. ## 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 '$\displaystyle \f(x)= \sqrt[5]{x^5+ x^4}$ for $\displaystyle x\ge 0$, Then would start by writing $\displaystyle x= (y^5+ y^4)^{1/2}$ then solve for y: $\displaystyle x^5= y^5+ y^5$ so $\displaystyle y^5+ y^4- x^5= 0$. Now, unfortunately, there is no simple "fifth degree equation formula" so there is no reasonable formula for solving that equation.

7. ## 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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### inverse operation of fifth root

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