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Stitz-Zeager_College_Algebra_e-book

15 and graph the function and its inverse on the same

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Unformatted text preview: 3 (x + 4)− 5 (x − 2) 3 ≥ 0 5 4. Show that x 3 2 2 3 2 2 2 1 = x for all x ≥ 0. 5. Verify the Quotient Rule for Radicals in Theorem 5.6. 1 3 − 3)− 3 + 4 x− 4 (x − 3) 3 < 0 x3 + 3x2 − 6x − 8 > x + 1 (r) x− 3 (x − 3)− 3 − x− 3 (x − 3)− 3 (x2 − 3x + 2) ≥ 0 (s) 1 322 Further Topics in Functions 6. Find the inverse of k (x) = √ 2x . x2 − 1 7. The period of a pendulum in seconds is given by T = 2π L g (for small displacements) where L is the length of the pendulum in meters and g = 9.8 meters per second per second is the acceleration due to gravity. My Seth-Thomas antique 1 schoolhouse clock needs T = 2 second and I can adjust the length of the pendulum via a small dial on the bottom of the bob. At what length should I set the pendulum? 8. The Cobb-Douglas production model states that the yearly total dollar value of the production output P in an economy is a function of labor x (the total number of hours worked in a year) and capital y (the total dollar value of all of the stuﬀ purchased in order to make things). Speciﬁcally, P = axb y 1−b . By ﬁxing P , we create what’s known as an ‘isoquant’ and we can then solve for y as...
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