Unformatted text preview: MAC1105: Quiz #18 Solutions
July 27, 2010 In the topright corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. Let f (x) = x + 3, g(x) = x2  1, and h(x) =
2x1 x+3 (a) Find (f h)(x), and state its domain. (f h)(x) = 2x  1, domain: (, 3) (3, ) (b) Find (f g)(x), and state its domain. (f g)(x) = f (g(x)) = f ( x2  1) = x2  1+3, domain: (, 1]
[1, ) (c) Find (g g)(x), and state its domain. (g g)(x) = g(g(x)) = g( x2 + 1) = domain: (,  2] [ 2, ) ( x2  1)2  1 = x2  2, (d) Find h1 (x).
y = 2x1 x = 2y1 (y + 3)x = 2y  1 xy + 3x = 2y  1 x+3 y+3 xy  2y = 3x  1 y(x  2) = 3x  1 y = 3x1 . So x2 h1 (x) = 3x1 . x2 2. Let f (x) and g(x) be given by the following tables:
x f (x) x g(x) 3 1 2 3 1 3 1 4 2 1 3 4 1 3 2 4 (a) Find (f g)(1). = f (g(1)) = f (3) = 1. (b) Find f 1 (3). f (1) = 3 f 1 (3) = 1. (c) Find (g f 1 )(4). = f (3) = 4 f 1 (4) = 3 g(f 1 (4)) = g(3) = 2. (d) Find (f f )(2). = f (f (2)) = f (1) = 3. (e) Find (g g g)(4). = g(g(g(4))) = g(g(4)) = g(4) = 4. 1 ...
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 Summer '10
 Picklesimer
 Algebra

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