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### 110Exam3W10

Course: MATH 110, Fall 2011
School: BYU
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Word Count: 684

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110 Math Exam 3: Winter 2010 4 Mar 2010 - 10 Mar 2010 1. Find the domain of the f g where f ( x) = (b) { x| x 3, x (c) { x| x 0, x 2/3} 2. Find the inverse of f ( x) = (c) f ( x) = 1 4 x 4 x+ x+2 4 3, x (f) { x| x 0} 0, x (e) { x| x 0} (b) f 1 ( x) = and g( x) = 2 . x (d) { x| x (a) { x| x (a) f 1 ( x) = x x+3 2 3} 3} 0, x 2/3} 4 x+2 . 2 (d) f 1 ( x) = 2 x 2 (e) f 1 ( x) = 3. Find...

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110 Math Exam 3: Winter 2010 4 Mar 2010 - 10 Mar 2010 1. Find the domain of the f g where f ( x) = (b) { x| x 3, x (c) { x| x 0, x 2/3} 2. Find the inverse of f ( x) = (c) f ( x) = 1 4 x 4 x+ x+2 4 3, x (f) { x| x 0} 0, x (e) { x| x 0} (b) f 1 ( x) = and g( x) = 2 . x (d) { x| x (a) { x| x (a) f 1 ( x) = x x+3 2 3} 3} 0, x 2/3} 4 x+2 . 2 (d) f 1 ( x) = 2 x 2 (e) f 1 ( x) = 3. Find the domain of h( x) = log3 2 x 4 (f) f ( x) = x 1 x x1 . (a) (0, ) (d) [0, 1) (b) (1, ) (e) (, 0] (1, ) (c) (, 0) (f) (, 0) (1, ) 1 4. Suppose that ln 7 = a and ln 2 = b. Express ln( 14 ) in terms of a and b. (a) a + b (d) (a + b) (b) 1 a b (e) 1 b (c) 1 a + b (f) 1 + a b 5. Solve 43 x = 32 for x. (a) x = (b) x = (c) x = (d) x = 5 6 2 3 1 2 6 5 (e) x = 2 (f) x = 1 3 2 6. Which of the following is equivalent to log5 9: (a) log5 36 log5 3 (d) log5 1 + log5 18 (b) log5 45 1 (e) 3 log5 3 (c) log5 1 + log5 3 (f) 1 + log5 3 7. Use properties of logarithms to the nd the exact value of log6 9 + log6 4. (a) 0 (d) 3 (b) 1 (e) 4 (c) 2 (f) none of the above 8. Express 21 log3 3 x + log3 (9 x2 ) log3 9 as a single logarithm. (a) log3 (81 x9 ) (b) 21 log3 ( 3 x + 9 x2 9) (c) log3 x (d) log3 x 9 +9 x 2 9 (e) log3 (9 x) 9 (f) none of the above 9. Solve log x + log( x + 15) = 2 for x. Recall that log x = log10 x. (a) x = (d) x = 5 1500 99 (b) x = 20 and x = 5 (e) x = 5 (c) x = 20 (f) no solution exists 10. Solve log2 ( x + 1) log4 x = 1 for x. (a) x = 1 (d) x = 1 (b) x = 0 (e) x = 2 (c) x = (f) no solution exists 1 2 11. Solve 2 log5 x = 3 log5 4 for x. (a) x = 16 (d) x = 8 (b) x = 16 (e) x = 8 (c) x = 16 (f) x = 8 2 12. Select the function that best ts the following graph. (a) y = ln( x) 1 (d) y = ln( x) + 1 (b) y = ln( x) (e) y = ln( x 1) (c) y = ln( x 1) (f) y = ln( x) + 2 2 3 13. ( Solve 2)2 x = 2 x for x (a) x = 1, x = (d) x = 2 3 (b) x = 1 (c) x = 2, x = 2 3 (e) x = 2 (f) x = 2, x = 1 3 2 3 14. The equation 32 x (4)3 x 2 = 5 has two solutions. Find the sum of the two solutions. (a) 0 (d) 3 (b) 1 (e) 4 (c) 2 (f) 5 15. How many years will it take for an initial investment of \$10,000 to grow to \$30,000? Assume a rate of interest of 10% compounded continuously. (a) ln 3 (d) 10 ln 3 (b) 100 ln 3 (e) 0.1 + ln 5 (c) ln 5 (f) 3 ln 3 10 16. What is the principal needed to get 1000 dollars after 2 years at 6% interest compounded monthly? (a) 1000 (1.005)24 (d) 1000 (0.995)12 (b) 1000 (1.005)12 (e) 1000 (0.995)24 (c) 1000 (1.005)24 (f) 1000 (1.005)12 17. A certain radioactive material decays according to the formula A(t) = A0 e0.0244t where t is in years and A0 is the initial amount of the material. What is the half life of this material? (a) ln 2 0.0244 (d) ln 2 0.0244 A0 ln 2 0.0488 (b) ln 2 (e) (c) 2(.0244) (f) none of the above 18. Find the vertex, focus, and directrix of the parabola (y 2)2 = 8( x + 1). (a) vertex (2,-1); focus (2,1); directrix x = 0 (b) vertex (2,-1); focus (1,2); directrix x = 3 (c) vertex (2,-1); focus (4,-1); directrix x = 0 (d) vertex (-1,2); focus (1,2); directrix x = 0 (e) vertex (-1,2); focus (1,2); directrix x = 3 (f) vertex (-1,2); focus (-1,4); directrix x = 4 19. Write the equation of a parabola with the focus at (-3,4) and directrix at the line y = 2. (a) ( x 3)2 = 4(y + 3) (d) ( x 3)2 = 4(y + 3) (b) ( x + 3)2 = 4(y 3) (e) ( x + 3)2 = 4(y + 3) (c) ( x + 3)2 = 4(y 3) (f) ( x 3)2 = 4(y 3) 20. Write the equation of a parabola that has vertex (0,0) and focus (4,0). (a) x2 = 16y (d) x2 = 16y (b) y2 = 8 x (e) x2 = 8y (c) y2 = 8 x (f) y2 = 16 x 4 1. c 2. a 3. f 4. d 5. a 6. b 7. c 8. c 9. e 10. d 11. f 12. a 13. a 14. b 15. d 16. c 17. d 18. e 19. b 20. f 5
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