Stitz-Zeager_College_Algebra_e-book

Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: f −1 . (b) Find the range of f by finding the domain of f −1 . 5x and h(x) = ex . Show that f = g ◦ h and that (g ◦ h)−1 = h−1 ◦ g −1 . (c) Let g (x) = x+1 9 7. With the help of your classmates, solve the inequality ex > xn for a variety of natural numbers n. What might you conjecture about the “speed” at which f (x) = ex grows versus any polynomial? 9 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. 6.3 Exponential Equations and Inequalities 6.3.2 367 Answers 1. (a) x = 4 ln(29) + ln(3) (b) x = ln(3) ln(3) (c) x = ln(3) − ln(2) ln(3) + 5 ln 1 2 (d) x = ln(3) − ln 1 2 7 (e) x = − 3 16 (f) x = 15 2 (g) x = − 11 1 (h) x = − 1 ln 1 = 4 ln(2) 8 4 4 ln(3) − 3 ln(7) (i) x = 7 ln(7) + 2 ln(3) 2. (a) (ln(53), ∞) ln(3) (b) ,∞ 12 ln(1.005) (c) (−∞, −1) ∪ (0, 1) (d) −∞, ln ln 2 5 4 5 3. (a) (2.3217, 4.3717) (b) x ≈ −0.76666, x = 2, x = 4 (c) x = 0 (j) t = ln(3) 12 ln(1.005) ln 1 2 −5730 (l) x = −1, 0, 1 (k) k = (m) x = ln(2) (n) t = 10 ln(18) 1 ln 29 −0.8 ln 2 5...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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