MATH 107 Name:________________________________ Directions: Fill out this answer sheet. Either select the correct answer or fill in the blank. Failure to use this answer sheet will result in an automatic 5 pt deduction. Create a single pdf file with this answer sheet first and any work you want me to consider for partial credit. Submit by Sunday (2/26/2017) 11:59 pm MDT. Section 5.1 (p. 369) Given f and g are the following functions: f ( x )=(x+1)2 ; g ( x )=3 x (fog)(2) 1. Find a. 32 c. 64 d. none of these (gof )( x ) 2. Find a. b. 49 2 x +2 x +1 b. 2 3x +1 c. 2 3 x +6 x +3 d. none of these Section 5.2 (p. 394) f ( x )=1 3. Which of the following is the inverse of a. f 1 ( x )=x 1 2 b. f 1 ( x )=x2 c. 12 x . 2 f 1 ( x )=x+ 1 d. none of these 4. Given that f(x) is an invertible function and f(5) = 2, can you find f-1(2)? If so, what is it? a. Not enough information b. 2 c. 5 d. none of these Section 0.9 (Ch. 0, p. 124) Find all real solutions. 5. 3 5 t 2+ 1=1 5. ____________ 1 MATH 107 Name:________________________________ 6. 2 x +1=3+ 4x 6.____________ 2 MATH 107 Name:________________________________ Section 5.3 (p. 407): 22, 23, 27, 38, 39, 42 7. Sketch the basic function and the translation: Basic function: f ( x )=x 3 ; Transformed function Solve the following: 8. 2 3 x =9 a. 36 b. 3 c. 27 d. 81 Section 6.1 (p. 429): Find the domain of the function and graph it. f ( x )=ln ( 4 x20 ) 3 f ( x )=(x3)31 MATH 107 Name:________________________________ Sketch the graph of g(x) by starting with the graph of f(x). f ( x )=2 x ; g ( x )=2x 1 Section 6.5 (p. 487): 36, 39, 40, 41 The current i measured in amps in a certain electronic circuit with a constant impressed 4 MATH 107 Name:________________________________ voltage of 120 volts is given by i ( t )=22e10 t where seconds after the circuit is switched on. Determine the value of i as t0 is the number of t . (This is called the steady state current.) The current in steady-state is approximately: a. b. c. d. 2 amps 2.1734 amps 2.2344 amps 3 amps BONUS: Worth 5 pts Directions: prove the following: If a function f is odd and invertible, prove that f^-1 (f inverse) is also odd. 5 MATH 107 Name:________________________________ Directions: Fill out this answer sheet. Either select the correct answer or fill in the blank. Failure to use this answer sheet will result in an automatic 5 pt deduction. Create a single pdf file with this answer sheet first and any work you want me to consider for partial credit. Submit by Sunday (2/26/2017) 11:59 pm MDT. Section 5.1 (p. 369) Given f and g are the following functions: f ( x )=(x+1)2 ; g ( x )=3 x (fog)(2) 1. Find a. 32 c. 64 d. none of these (gof )( x ) 2. Find a. b. 49 2 x +2 x +1 b. 2 3x +1 c. 2 3 x +6 x +3 d. none of these Section 5.2 (p. 394) f ( x )=1 3. Which of the following is the inverse of a. f 1 ( x )=x 1 2 b. f 1 ( x )=x2 c. 12 x . 2 f 1 ( x )=x+ 1 d. none of these 4. Given that f(x) is an invertible function and f(5) = 2, can you find f-1(2)? If so, what is it? a. Not enough information b. 2 c. 5 d. none of these Section 0.9 (Ch. 0, p. 124) Find all real solutions. 5. 3 5 t 2+ 1=1 5. 3 7 , 3 7 3 5 t 2+ 1=1 1 MATH 107 Name:________________________________ 6. 3 t2 +1=4 t 2 +1=4 3=64 t =641=63 t= 63=3 7+3 7 2 2 x +1=3+ 4x 6. 4 2 x +1=3+ 4x 2 2 x +1= ( 3+ 4x ) =9+ 6 4x+ 4x=13+6 4xx 3 x12=6 4x 3 x12=6 4x ( 3 x12 )2=36 ( 4x ) 9 x 72 x +144=14436 x 9 x 236 x=0 9 x( x4 ) =0 x=04 2 Note that x = 0 does not satisfy the solution so the only solution is x = 4. 2 MATH 107 Name:________________________________ Section 5.3 (p. 407): 22, 23, 27, 38, 39, 42 7. Sketch the basic function and the translation: Basic function: f ( x )=x 3 ; Transformed function f ( x )=(x3)31 Green curve (f) is the Basic function and the red curve (g) is Transformed function. Solve the following: 2 8. x 3 =9 a. 36 b. 3 c. 27 d. 81 3 MATH 107 Name:________________________________ Section 6.1 (p. 429): Find the domain of the function and graph it. f ( x )=ln ( 4 x20 ) 5 Solution: x > 5 Interval notation: (5, +) Sketch the graph of g(x) by starting with the graph of f(x). f ( x )=2 x ; g ( x )=2x 1 4 MATH 107 Name:________________________________ Blue curve is the f(x) and the orange curve is g(x). Section 6.5 (p. 487): 36, 39, 40, 41 The current i measured in amps in a certain electronic circuit with a constant impressed voltage of 120 volts is given by 10 t i ( t )=22e where seconds after the circuit is switched on. Determine the value of steady state current.) The current in steady-state is approximately: a. b. c. d. 2 amps 2.1734 amps 2.2344 amps 3 amps BONUS: 5 i as t0 is the number of t . (This is called the MATH 107 Name:________________________________ Worth 5 pts Directions: prove the following: If a function f is odd and invertible, prove that f^-1 (f inverse) is also odd. Proof: As f is invertible so, f(x) = y x = f-1(y) -x = - f-1(y); Multiply both sides by -1. Again as f is an odd function so, f(-x) = -y -x = f-1(-y) = - f-1(y) f-1(-y) = - f-1(y) Therefore f^-1 (f inverse) is also odd. 6 MATH 107 Name:________________________________ Directions: Fill out this answer sheet. Either select the correct answer or fill in the blank. Failure to use this answer sheet will result in an automatic 5 pt deduction. Create a single pdf file with this answer sheet first and any work you want me to consider for partial credit. Submit by Sunday (2/26/2017) 11:59 pm MDT. Section 5.1 (p. 369) Given f and g are the following functions: ( ) 1. Find ( ) ( ) )( ) a. 32 2. Find ( ( b. 49 c. 64 d. none of these )( ) a. b. +1 c. d. none of these Section 5.2 (p. 394) 3. Which of the following is the inverse of ( ) a. b. ( ) . c. ( ) ( ) d. none of these 4. Given that f(x) is an invertible function and f(5) = 2, can you find f -1(2)? If so, what is it? a. Not enough information b. 2 c. 5 d. none of these Section 0.9 (Ch. 0, p. 124) Find all real solutions. 5. 5. 1 MATH 107 Name:________________________________ 6. ( ( ) ) ( 6. 4 ( ) ) Note that x = 0 does not satisfy the solution so the only solution is x = 4. 2 MATH 107 Name:________________________________ Section 5.3 (p. 407): 22, 23, 27, 38, 39, 42 7. Sketch the basic function and the translation: Basic function: ( ) ; Transformed function ( ) ( ) Green curve (f) is the Basic function and the red curve (g) is Transformed function. Solve the following: 8. a. 36 b. 3 c. 27 d. 81 Section 6.1 (p. 429): Find the domain of the function and graph it. 3 MATH 107 Name:________________________________ ( ) ( ) 5 Solution: x > 5 Interval notation: (5, +) Sketch the graph of g(x) by starting with the graph of f(x). ( ) ( ) Blue curve is the f(x) and the orange curve is g(x). 4 MATH 107 Name:________________________________ Section 6.5 (p. 487): 36, 39, 40, 41 The current measured in amps in a certain electronic circuit with a constant impressed voltage of 120 volts is given by ( ) where is the number of seconds after the circuit is switched on. Determine the value of as . (This is called the steady state current.) The current in steady-state is approximately: a. b. c. d. 2 amps 2.1734 amps 2.2344 amps 3 amps BONUS: Worth 5 pts Directions: prove the following: If a function f is odd and invertible, prove that f^-1 (f inverse) is also odd. Proof: As f is invertible so, f(x) = y x = f-1(y) -x = - f-1(y); Multiply both sides by -1. Again as f is an odd function so, f(-x) = -y -x = f-1(-y) = - f-1(y) f-1(-y) = - f-1(y) Therefore f^-1 (f inverse) is also odd. 5 MATH 107 Name:________________________________ Directions: Fill out this answer sheet. Either select the correct answer or fill in the blank. Failure to use this answer sheet will result in an automatic 5 pt deduction. Create a single pdf file with this answer sheet first and any work you want me to consider for partial credit. Submit by Sunday (2/26/2017) 11:59 pm MDT. Section 5.1 (p. 369) Given f and g are the following functions: f ( x )=(x+1)2 ; g ( x )=3 x (fog)(2) 1. Find a. 32 c. 64 d. none of these (gof )( x ) 2. Find a. b. 49 2 x +2 x +1 b. 2 3x +1 c. 2 3 x +6 x +3 d. none of these Section 5.2 (p. 394) f ( x )=1 3. Which of the following is the inverse of a. f 1 ( x )=x 1 2 b. f 1 ( x )=x2 c. 12 x . 2 f 1 ( x )=x+ 1 d. none of these 4. Given that f(x) is an invertible function and f(5) = 2, can you find f-1(2)? If so, what is it? a. Not enough information b. 2 c. 5 d. none of these Section 0.9 (Ch. 0, p. 124) Find all real solutions. 5. 3 5 t 2+ 1=1 5. 3 7 , 3 7 3 5 t 2+ 1=1 1 MATH 107 Name:________________________________ 6. 3 t2 +1=4 t 2 +1=4 3=64 t =641=63 t= 63=3 7+3 7 2 2 x +1=3+ 4x 6. 4 2 x +1=3+ 4x 2 2 x +1= ( 3+ 4x ) =9+ 6 4x+ 4x=13+6 4xx 3 x12=6 4x 3 x12=6 4x ( 3 x12 )2=36 ( 4x ) 9 x 72 x +144=14436 x 9 x 236 x=0 9 x( x4 ) =0 x=04 2 Note that x = 0 does not satisfy the solution so the only solution is x = 4. 2 MATH 107 Name:________________________________ Section 5.3 (p. 407): 22, 23, 27, 38, 39, 42 7. Sketch the basic function and the translation: Basic function: f ( x )=x 3 ; Transformed function f ( x )=(x3)31 Green curve (f) is the Basic function and the red curve (g) is Transformed function. Solve the following: 2 8. x 3 =9 a. 36 b. 3 c. 27 d. 81 3 MATH 107 Name:________________________________ Section 6.1 (p. 429): Find the domain of the function and graph it. f ( x )=ln ( 4 x20 ) 5 Solution: x > 5 Interval notation: (5, +) Sketch the graph of g(x) by starting with the graph of f(x). f ( x )=2 x ; g ( x )=2x 1 4 MATH 107 Name:________________________________ Blue curve is the f(x) and the orange curve is g(x). Section 6.5 (p. 487): 36, 39, 40, 41 The current i measured in amps in a certain electronic circuit with a constant impressed voltage of 120 volts is given by 10 t i ( t )=22e where seconds after the circuit is switched on. Determine the value of steady state current.) The current in steady-state is approximately: a. b. c. d. 2 amps 2.1734 amps 2.2344 amps 3 amps BONUS: 5 i as t0 is the number of t . (This is called the MATH 107 Name:________________________________ Worth 5 pts Directions: prove the following: If a function f is odd and invertible, prove that f^-1 (f inverse) is also odd. Proof: As f is invertible so, f(x) = y x = f-1(y) -x = - f-1(y); Multiply both sides by -1. Again as f is an odd function so, f(-x) = -y -x = f-1(-y) = - f-1(y) f-1(-y) = - f-1(y) Therefore f^-1 (f inverse) is also odd. 6 MATH 107 Name:________________________________ Directions: Fill out this answer sheet. Either select the correct answer or fill in the blank. Failure to use this answer sheet will result in an automatic 5 pt deduction. Create a single pdf file with this answer sheet first and any work you want me to consider for partial credit. Submit by Sunday (2/26/2017) 11:59 pm MDT. Section 5.1 (p. 369) Given f and g are the following functions: ( ) 1. Find ( ) ( ) )( ) a. 32 2. Find ( ( b. 49 c. 64 d. none of these )( ) a. b. +1 c. d. none of these Section 5.2 (p. 394) 3. Which of the following is the inverse of ( ) a. b. ( ) . c. ( ) ( ) d. none of these 4. Given that f(x) is an invertible function and f(5) = 2, can you find f -1(2)? If so, what is it? a. Not enough information b. 2 c. 5 d. none of these Section 0.9 (Ch. 0, p. 124) Find all real solutions. 5. 5. 1 MATH 107 Name:________________________________ 6. ( ( ) ) ( 6. 4 ( ) ) Note that x = 0 does not satisfy the solution so the only solution is x = 4. 2 MATH 107 Name:________________________________ Section 5.3 (p. 407): 22, 23, 27, 38, 39, 42 7. Sketch the basic function and the translation: Basic function: ( ) ; Transformed function ( ) ( ) Green curve (f) is the Basic function and the red curve (g) is Transformed function. Solve the following: 8. a. 36 b. 3 c. 27 d. 81 Section 6.1 (p. 429): Find the domain of the function and graph it. 3 MATH 107 Name:________________________________ ( ) ( ) 5 Solution: x > 5 Interval notation: (5, +) Sketch the graph of g(x) by starting with the graph of f(x). ( ) ( ) Blue curve is the f(x) and the orange curve is g(x). 4 MATH 107 Name:________________________________ Section 6.5 (p. 487): 36, 39, 40, 41 The current measured in amps in a certain electronic circuit with a constant impressed voltage of 120 volts is given by ( ) where is the number of seconds after the circuit is switched on. Determine the value of as . (This is called the steady state current.) The current in steady-state is approximately: a. b. c. d. 2 amps 2.1734 amps 2.2344 amps 3 amps BONUS: Worth 5 pts Directions: prove the following: If a function f is odd and invertible, prove that f^-1 (f inverse) is also odd. Proof: As f is invertible so, f(x) = y x = f-1(y) -x = - f-1(y); Multiply both sides by -1. Again as f is an odd function so, f(-x) = -y -x = f-1(-y) = - f-1(y) f-1(-y) = - f-1(y) Therefore f^-1 (f inverse) is also odd. 5