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

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