1. Explain why we cannot find inverse functions for all polynomial functions.
2. Why must we restrict the domain of a quadratic function when finding its inverse?
3. When finding the inverse of a radical function, what restriction will we need to make?
4. The inverse of a quadratic function will always take what form?
For the following exercises, find the inverse of the function on the given domain.
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For the following exercises, find the inverse of the functions.
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For the following exercises, find the inverse of the functions.
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For the following exercises, find the inverse of the function and graph both the function and its inverse.
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For the following exercises, use a graph to help determine the domain of the functions.
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For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on the graph of the inverse with y-coordinates given.
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For the following exercises, find the inverse of the functions with a, b, c positive real numbers.
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For the following exercises, determine the function described and then use it to answer the question.
57. An object dropped from a height of 200 meters has a height, , in meters after t seconds have lapsed, such that . Express t as a function of height, h, and find the time to reach a height of 50 meters.
58. An object dropped from a height of 600 feet has a height, , in feet after t seconds have elapsed, such that . Express t as a function of height h, and find the time to reach a height of 400 feet.
59. The volume, V, of a sphere in terms of its radius, r, is given by . Express r as a function of V, and find the radius of a sphere with volume of 200 cubic feet.
60. The surface area, A, of a sphere in terms of its radius, r, is given by . Express r as a function of V, and find the radius of a sphere with a surface area of 1000 square inches.
61. A container holds 100 ml of a solution that is 25 ml acid. If n ml of a solution that is 60% acid is added, the function gives the concentration, C, as a function of the number of ml added, n. Express n as a function of C and determine the number of mL that need to be added to have a solution that is 50% acid.
62. The period T, in seconds, of a simple pendulum as a function of its length l, in feet, is given by . Express l as a function of T and determine the length of a pendulum with period of 2 seconds.
63. The volume of a cylinder, V, in terms of radius, r, and height, h, is given by . If a cylinder has a height of 6 meters, express the radius as a function of V and find the radius of a cylinder with volume of 300 cubic meters.
64. The surface area, A, of a cylinder in terms of its radius, r, and height, h, is given by . If the height of the cylinder is 4 feet, express the radius as a function of V and find the radius if the surface area is 200 square feet.
65. The volume of a right circular cone, V, in terms of its radius, r, and its height, h, is given by . Express r in terms of h if the height of the cone is 12 feet and find the radius of a cone with volume of 50 cubic inches.
66. Consider a cone with height of 30 feet. Express the radius, r, in terms of the volume, V, and find the radius of a cone with volume of 1000 cubic feet.
Candela Citations
- Precalculus. Authored by: Jay Abramson, et al.. Provided by: OpenStax. Located at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.. License: CC BY: Attribution. License Terms: Download for free at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.