{"id":1927,"date":"2016-11-02T22:17:45","date_gmt":"2016-11-02T22:17:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&p=1927"},"modified":"2025-10-13T20:44:27","modified_gmt":"2025-10-13T20:44:27","slug":"introduction-radical-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/chapter\/introduction-radical-functions\/","title":{"raw":"Introduction to Radical Functions","rendered":"Introduction to Radical Functions"},"content":{"raw":"

What you'll learn to do: Evaluate the inverse of polynomial and radical functions<\/h2>\r\nA mound of gravel is in the shape of a cone with the height equal to twice the radius.\r\n\r\n\"Gravel\r\n\r\nThe volume is found using a formula from geometry.\r\n

[latex]\\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}[\/latex]<\/p>\r\nWe have written the volume [latex]V[\/latex]\u00a0in terms of the radius [latex]r[\/latex]. 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\r\n

[latex]r=\\sqrt[3]{\\dfrac{3V}{2\\pi }}[\/latex]<\/p>\r\nThis function is the inverse of the formula for [latex]V[\/latex]\u00a0in terms of [latex]r[\/latex].\r\n\r\nIn this section, we will explore the inverses of polynomial and rational functions and in particular the radical functions we encounter in the process.","rendered":"

What you’ll learn to do: Evaluate the inverse of polynomial and radical functions<\/h2>\n

A mound of gravel is in the shape of a cone with the height equal to twice the radius.<\/p>\n

\"Gravel<\/p>\n

The volume is found using a formula from geometry.<\/p>\n

[latex]\\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}[\/latex]<\/p>\n

We have written the volume [latex]V[\/latex]\u00a0in terms of the radius [latex]r[\/latex]. 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<\/p>\n

[latex]r=\\sqrt[3]{\\dfrac{3V}{2\\pi }}[\/latex]<\/p>\n

This function is the inverse of the formula for [latex]V[\/latex]\u00a0in terms of [latex]r[\/latex].<\/p>\n

In this section, we will explore the inverses of polynomial and rational functions and in particular the radical functions we encounter in the process.<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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CC licensed content, Original<\/div>