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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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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