Solution Start with the given function for V. Notice that the meaningful domain for the function is 7 > 0 since negative radii would not make sense in this context nor would a radius of 0 . Also note the range of the function (hence, the domain of the inverse function) is V 2 0. Solve for r in terms of V, using the method outlined previously. Note that in real-world applications, we do not swap the variables when finding inverses. Instead, we change which variable is considered to be the independent variable. V = 2 73 = 3V 2 7T Solve for 73 . T = 3 3V Solve for T. This is the result stated in the section opener. Now evaluate this for V = 100 and 7 = 3.14. T = 3/ 3V / 3-100 2.3.14 ~ V47.7707 ~3.63snhu.mobius.cloud C 5.7 Inverses and Radical Functions - Algebra and Trigonometry | OpenStax Solving Applications of Radical Functions Radical functions are common in physical models, as we saw in the section opener. We now have enough tools to be able to solve the problem posed at the start of the section. Example 6 Solving an Application with a Cubic Function A mound of gravel is in the shape of a cone with the height equal to twice the radius. The volume of the cone in terms of the radius is given by Find the inverse of the function V = 2 wr that determines the volume V of a cone and is a function of the radius r. Then use the inverse function to calculate the radius of such a mound of gravel measuring 100 cubic feet. Use n = 3.14. Solution Start with the given function for V. Notice that the meaningful domain for the function is r > 0 since negative radii would not make sense in this context nor would a radius of 0. Also note the range of the function (hence, the domain of the inverse function) is V 2 0. Solve for r in terms of V, using the method outlined previously. Note that in real-world applications, we do not swap the variables when finding inverses. Instead, we change which variable is considered to be the independent variable. 3V Solve for ,3