Unformatted text preview: (x) = H (f (G(x))) where
1
G(x) = 2x − 7 and H (x) = − 2 x + 1. 8. (a) h(x) = (g ◦ f ) (x) where f (x) = 2x − 1
√
and g (x) = x. (c) F (x) = (g ◦ f ) (x) where f (x) = x2 − 1
and g (x) = x3 . (b) r(x) = (g ◦ f ) (x) where f (x) = 5x + 1
2
and g (x) = .
x (d) R(x) = (g ◦ f ) (x) where f (x) = x3 and
2x + 1
g (x) =
.
x−1 9. F (x) = √
x3 + 6
x+6
= (h(g (f (x))) where f (x) = x3 , g (x) =
and h(x) = x.
x3 − 9
x−9 10. V (x) = x3 so V (x(t)) = (t + 1)3
11. (a) R(x) = 2x
(b) (R ◦ x) (t) = −8t2 + 40t + 184, 0 ≤ t ≤ 4. This gives the revenue per hour as a function
of time.
(c) Noon corresponds to t = 2, so (R ◦ x) (2) = 232. The hourly revenue at noon is $232
per hour. 6 The quantity −x4 + 18x2 − 72 is a ‘quadratic in disguise’ which factors nicely. See Example 3.3.4 is Section 3.3. 5.2 Inverse Functions 5.2 293 Inverse Functions Thinking of a function as a process like we did in Section 1.5, in this section we seek another
function which might reverse that process. As in real li...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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