Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: f −1 . x (c) Let g (x) = and h(x) = log(x). Show that f = g ◦ h and (g ◦ h)−1 = h−1 ◦ g −1 . 1−x (We know this is true in general by Exercise 8 in Section 5.2, but it’s nice to see a specific example of the property.) 376 7. Let f (x) = Exponential and Logarithmic Functions 1 ln 2 1+x . Compute f −1 (x) and find its domain and range. 1−x 8. Explain the equation in Exercise 1g and the inequality in Exercise 2b above in terms of the Richter scale for earthquake magnitude. (See Exercise 6a in Section 6.1.) 9. Explain the equation in Exercise 1i and the inequality in Exercise 2c above in terms of sound intensity level as measured in decibels. (See Exercise 6b in Section 6.1.) 10. Explain the equation in Exercise 1h and the inequality in Exercise 2d above in terms of the pH of a solution. (See Exercise 6c in Section 6.1.) √ 11. With the help of your classmates, solve the inequality n x > ln(x) for a variety of natural numbers n. What might you conjecture about the “speed” a...
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