Introduction to Radical Functions
What you’ll learn to do: Evaluate the inverse of polynomial and radical functions
A mound of gravel is in the shape of a cone with the height equal to twice the radius.
The volume is found using a formula from geometry.
\begin{align}V&=\frac{1}{3}\pi {r}^{2}h \\[1mm] &=\frac{1}{3}\pi {r}^{2}\left(2r\right) \\[1mm] &=\frac{2}{3}\pi {r}^{3} \end{align}
We have written the volume in terms of the radius . 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 formulaThis function is the inverse of the formula for in terms of . In this section, we will explore the inverses of polynomial and rational functions and in particular the radical functions we encounter in the process.
