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Stitz-Zeager_College_Algebra_e-book

Proceeding as above we nd that n xy n x n y the

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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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