# Introduction to Radical Functions

### Learning Objectives

By the end of this lesson, you will be able to:- Find the inverse of a polynomial function.
- Restrict the domain to find the inverse of a polynomial function.

[latex]\begin{array}{l}V=\frac{1}{3}\pi {r}^{2}h\hfill \\ \text{ }=\frac{1}{3}\pi {r}^{2}\left(2r\right)\hfill \\ \text{ }=\frac{2}{3}\pi {r}^{3}\hfill \end{array}[/latex]

We have written the volume*V*in terms of the radius

*r*. However, in some cases, we may start out with the volume and want to find the radius. For example: A customer purchases 100 cubic feet of gravel to construct a cone shape mound with a height twice the radius. What are the radius and height of the new cone? To answer this question, we use the formula

[latex]r=\sqrt[3]{\frac{3V}{2\pi }}[/latex]

This function is the inverse of the formula for*V*in terms of

*r*. In this section, we will explore the inverses of polynomial and rational functions and in particular the radical functions we encounter in the process.

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### CC licensed content, Original

- Revision and Adaptation.
**Provided by:**Lumen Learning**License:**CC BY: Attribution.

### CC licensed content, Shared previously

- Precalculus.
**Provided by:**OpenStax**Authored by:**Jay Abramson, et al..**Located at:**https://openstax.org/books/precalculus/pages/1-introduction-to-functions.**License:**CC BY: Attribution.**License terms:**Download For Free at : http://cnx.org/contents/[email protected].. - College Algebra.
**Provided by:**OpenStax**Authored by:**Abramson, Jay et al..**License:**CC BY: Attribution.**License terms:**Download for free at http://cnx.org/contents/[email protected].