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Stitz-Zeager_College_Algebra_e-book

# 3 analytically show that the function f x x3 3x 1 is

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Unformatted text preview: x) (g) (f ◦ f ) (x) (h) (g ◦ g ) (x) (i) (h ◦ h) (x) √ 4. Let f (x) = 9 − x2 and g (x) = x2 − 9. Find and simplify the indicated composite functions. State the domain of each. (a) (f ◦ f )(x) (c) (g ◦ f )(x) (b) (g ◦ g )(x) (d) (f ◦ g )(x) 290 Further Topics in Functions 5. Let f be the function deﬁned by f = {(−3, 4), (−2, 2), (−1, 0), (0, 1), (1, 3), (2, 4), (3, −1)} and let g be the function deﬁned g = {(−3, −2), (−2, 0), (−1, −4), (0, 0), (1, −3), (2, 1), (3, 2)}. Find the each of the following values if it exists. (a) (b) (c) (d) (e) (f) (g) (h) (g ◦ f )(−2) (f ◦ g )(3) f (g (−1)) (f ◦ f )(0) (f ◦ g )(−3) (g ◦ f )(3) g (f (−3)) (g ◦ g )(−2) (i) g (f (g (0))) (j) f (f (f (−1))) (k) f (f (f (f (f (1))))) n times (l) (g ◦ g ◦ · · · ◦ g )(0) 6. Let g (x) = −x, h(x) = x + 2, j (x) = 3x and k (x) √ x − 4. In what order must these functions = √ be composed with f (x) = x to create F (x) = 3 −x + 2 − 4? 7. What linear functions could be u...
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