Stitz-Zeager_College_Algebra_e-book

# 3 311 other algebraic functions this section serves

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Unformatted text preview: tes how ‘real-world’ processes such as ﬁlling out federal income tax forms or computing your ﬁnal course grade could be viewed as a use of function composition. Find a process for which composition with itself (iteration) makes sense. 5.1 Function Composition 5.1.2 291 Answers 1 x Domain: (0, ∞) 1. (a) (f ◦ g )(x) = 3|x| − 6 Domain: (−∞, ∞) (i) (h ◦ k )(x) = (b) (g ◦ f )(x) = |3x − 6| Domain: (−∞, ∞) √ (c) (f ◦ h)(x) = 3 x − 6 Domain: [0, ∞) √ (d) (h ◦ f )(x) = 3x − 6 Domain: [2, ∞) √ (e) (g ◦ h)(x) = x Domain: [0, ∞) 1 (j) (k ◦ h)(x) = √ x Domain: (0, ∞) √ (k) (f ◦ g ◦ h)(x) = 3 x − 6 Domain: [0, ∞) (f) (h ◦ g )(x) = |x| Domain: (−∞, ∞) 3 (g) (f ◦ k )(x) = − 6 x Domain: (−∞, 0) ∪ (0, ∞) 1 (h) (k ◦ f )(x) = 3x − 6 Domain: (−∞, 2) ∪ (2, ∞) 2. (a) (g ◦ f ) (x) = 4x2 + 2x − 6 Domain: (−∞, ∞) 2x + 7 2x − 5 Domain: −∞, 5 ∪ 2 1 x Domain: (−∞, 0) ∪ (0, ∞) (l) (h ◦ g ◦ k )(x) = (b) (...
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