Quiz18solutions - MAC1105: Quiz #18 Solutions July 27, 2010...

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Unformatted text preview: MAC1105: Quiz #18 Solutions July 27, 2010 In the top-right 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) = 2x-1 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 h-1 (x). y = 2x-1 x = 2y-1 (y + 3)x = 2y - 1 xy + 3x = 2y - 1 x+3 y+3 xy - 2y = -3x - 1 y(x - 2) = -3x - 1 y = -3x-1 . So x-2 h-1 (x) = -3x-1 . x-2 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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