hw12 - padilla (tp5647) Homework12 Fouli (58320) This...

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Unformatted text preview: padilla (tp5647) Homework12 Fouli (58320) This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points 003 10.0 points 1 Find the value of f (0) when f (t) = 4 sin 2t , 1. f (0) = 2 2. f (0) = 4 3. f (0) = 1 4. f (0) = 3 5. f (0) = 5 004 10.0 points f 2 = 6. Find all functions g such that 4x2 + 5x + 4 . g (x) = x 1. g(x) = x 4x2 + 5x + 4 + C 2. g(x) = 2 x 4x2 + 5x - 4 + C 3. g(x) = 2 x 4. g(x) = x 4 2 5 x + x-4 +C 5 3 4 2 5 x + x+4 +C 5 3 Consider the following functions: sin2 x , 2 cos 2x (B) F2 (x) = - , 4 cos2 x . (C) F3 (x) = 2 Which are anti-derivatives of (A) F1 (x) = f (x) = sin x cos x ? 1. F1 only 5. g(x) = 2 x 4x2 + 5x + 4 + C 6. g(x) = 2 x 002 4 2 5 x + x+4 +C 5 3 10.0 points Determine f (t) when f (t) = 4(3t + 1) and f (1) = 2, f (1) = 5 . 2. F2 only 3. F1 and F2 only 4. F2 and F3 only 5. all of them 6. F3 only 7. none of them 8. F1 and F3 only 005 10.0 points 1. f (t) = 2t3 + 2t2 - 8t + 9 2. f (t) = 2t3 - 4t2 + 8t - 1 3. f (t) = 6t3 - 4t2 + 8t - 5 4. f (t) = 6t + 4t - 8t + 3 5. f (t) = 6t3 + 2t2 - 8t + 5 6. f (t) = 2t3 - 2t2 + 8t - 3 3 2 padilla (tp5647) Homework12 Fouli (58320) Find f (/2) when 1 2 f (t) = 3 cos t - 4 sin t 3 3 and f (0) = -1. 1. f (/2) = 1 2 1. F (3) = 2. F (3) = 3. F (3) = 4. F (3) = 61 4 63 4 31 2 65 4 2 7 2 5 3. f (/2) = - 2 3 4. f (/2) = - 2 1 5. f (/2) = - 2 2. f (/2) = - 006 10.0 points 5. F (3) = 16 008 10.0 points Let f be a twice-differentiable function and let g be its inverse. Consider the following equations: A. g(f (x)) = x, f (g(x)) = x ; A particle moves along the x-axis so that its acceleration at time t is a(t) = 9 - 4t in units of feet and seconds. If the velocity of the particle at t = 0 is 5 ft/sec, how many seconds will it take for the particle to reach its furthest point to the right? 1. 3 seconds 2. 5 seconds 3. 2 seconds 4. 4 seconds B. f (g(x))(g (x))2 + f (g(x))g (x) = 0 ; C. g (x) = f (g(x)) . Which ones do f, g satisfy? 1. A and C only 2. none of them 3. all of them 4. B only 5. C only 6. A and B only 5. 1 seconds 007 10.0 points 7. B and C only 8. A only 009 10.0 points If F = F (x) is the unique anti-derivative of f (x) = (4 - x)2 - 7 (4 - x)2 Find the value of g (-1) when g is the inverse of the function f (x) = 2 sin x, -/2 x /2 . which satisfies F (0) = 0, find F (3). padilla (tp5647) Homework12 Fouli (58320) 1. g (-1) = -1 1 2. g (-1) = 2 1 3. g (-1) = - 2 1 4. g (-1) = 3 1 5. g (-1) = - 3 3 3. g (6) = 1 4. g (6) = 5. g (6) = 2 6 012 10.0 points Find the value of g (-2) when g is the inverse of the function f defined by f (x) = 3 x3 - (Hint: f (-1) = -2.) 1. g (-2) = -3 2. g (-2) = 1 10 1 10 1 . x 6. g (-1) = 1 010 10.0 points Suppose g is the inverse function of a differ1 . entiable function f and G(x) = g(x) 1 If f (5) = 7 and f (5) = , find G (7). 25 1. G (7) = 4 2. G (7) = 3 3. G (7) = -1 4. G (7) = -4 5. G (7) = -7 011 10.0 points 3. g (-2) = - 4. g (-2) = 3 5. g (-2) = -10 6. g (-2) = 10 013 10.0 points Find the inverse of f (x) = x 2 9x - 1 5x + 4 9x - 1 4x + 5 9x + 1 4x + 5 5x - 1 4x + 9 1 + 5x . 9 - 4x On (-1, 1) the function f (x) = 6 + x2 + tan 1. f -1(x) = 2. f -1(x) = 3. f -1(x) = 4. f -1(x) = has an inverse g. Find the value of g (6). (Hint: find the value of f (0)). 1. g (6) = 2. g (6) = 6 2 padilla (tp5647) Homework12 Fouli (58320) 5. f -1 (x) = 9x + 1 5x + 4 10.0 points 016 10.0 points 4 014 Find the inverse function, f -1, for f when f (x) = 9 - x2 , 9 - x2 , x2 - 9, 1 , 9 - x2 0 x 3. -3 x 3 -3 x 3 0x<3 Find the inverse function, f -1 , of f (x) = 1. f -1 (x) = 2x . 3 x2 + 16 1. f -1(x) = 2. f -1(x) = 3. f -1(x) = 4 - 3 x2 3x 4x 4 - 3 x2 2. f -1 (x) = 3 3. f -1 (x) = 4 - 16 x2 4 + 3 x2 -1 4. f (x) = 4x 4 - 16 x2 5. f -1 (x) = 3 6. f -1 (x) = 015 4x 4 + 3 x2 10.0 points 4. inverse doesn't exist 5. f -1(x) = 017 9 - x2 , 0x3 10.0 points Which of the following functions will fail to have an inverse? Find the inverse function, f -1 , of f when f is defined by f (x) = 7x - 2 , 2 x . 7 2 7 1. f -1 (x) = 2. f -1 (x) = 3. f -1 1 2 ( x - 7), x 2 1 7 x2 - 2, x 0 x2 + 7, x 7 2 7 2 4 1.3 2 1 0 -1 -2 -3 -4 -5 4 2.3 2 1 0 -1 -2 -3 -4 -5 4 2 -4 -2 -2 -4 2 4 1 (x) = 2 -5 -4 -3 -2 -1 0 1 2 3 4 4 2 -4 -2 -2 -4 2 4 4. f -1 (x) = 5. f 6. f -1 1 2 ( x + 2), x 7 1 (x) = ( x2 + 2), x 0 7 1 (x) = 2 x2 - 7, x 0 -1 -5 -4 -3 -2 -1 0 1 2 3 4 padilla (tp5647) Homework12 Fouli (58320) 5 4 3.3 2 1 0 -1 -2 -3 -4 -5 4 5 4 2 -4 -2 -2 -4 2 4 -5 -4 -3 -2 -1 0 1 2 3 4 10 9 8 7 1. 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 10 9 8 7 2. 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 10 9 8 7 3. 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 8 4 -8 -4 4 -4 -8 -10 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 8 4.3 2 1 0 -1 -2 -3 -4 -5 4 5.3 2 1 0 -1 -2 -3 -4 -5 4 2 -4 -2 -2 -4 2 4 8 4 -8 -4 4 -4 -8 -10 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 -5 -4 -3 -2 -1 0 1 2 3 4 8 4 2 -4 -2 -2 -4 2 4 8 4 -8 -4 4 -4 -8 -10 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 -5 -4 -3 -2 -1 0 1 2 3 4 018 10.0 points 8 If the graph of f is 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 8 4 -8 -4 -4 -8 -10 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 9 8 7 4. 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 8 4 -8 -4 4 -4 -8 -10 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 4 8 8 which of the following is the graph of f -1 (x)? padilla (tp5647) Homework12 Fouli (58320) 10 9 8 7 5. 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 6 8 4 -8 -4 4 -4 -8 -10 -9-8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 021 10.0 points Consider the following properties that a function f might have: 8 A. graph of f passes vertical line test; B. f is 1 - 1; C. f (x) > 0 for all x. Which properties always ensure that f has an inverse f -1 ? 1. A and C only 2. B only 3. none of them 4. A only 5. all of them 6. A and B only 7. C only 019 10.0 points Consider the following functions: 1 F1 (x) = |x + 2 |, -1 x 1 , -1 x 1 , -/4 x /4 . F2 (x) = x2 + x, F3 (x) = sin 2x, Which have an inverse on the given domain? 1. F2 only 2. F1 only 3. F1 and F3 only 4. F2 and F3 only 5. all of them 6. F1 and F2 only 7. F3 only 8. none of them 020 10.0 points 8. B and C only 022 10.0 points If the graph of f is Use f (x) to determine whether f (x) = x4 - 2x2 4 has an inverse on (-, ). 1. f does not have inverse 2. f has inverse which one of the following contains only graphs of anti-derivatives of f ? padilla (tp5647) Homework12 Fouli (58320) 7 1. 6. 2. 3. 4. 5. ...
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This note was uploaded on 09/09/2009 for the course M 408k taught by Professor Fouli during the Spring '09 term at University of Texas-Tyler.

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