IAT SOLUTIONS - C_7.pdf

Chapter 7, continued43.44.45.y121 xy123 xDomain: all real numbersRange: y > 0Domain: all real numbersRange: y < 0y Domain: all real numbersRange: y > 0Lesson 7.37.3 Guided Practice (pp. 493–495)1. e 7 p e 4 5 e 7 1 4 5 e 112. 2e 23 p 6e 5 5 12e 23 1 5 5 12e 23. 24e8 }4e 5 5 6e8 2 5 5 6e 34. (10e 24x ) 3 5 10 3 (e 24x ) 3 5 1000e 212x 5 1000 }e 12x5. e 3/4 ø 2.1176.1yDomain: all real numbersRange: y > 0Copyright © by McDougal Littell, a division of Houghton Mifflin Company.121 x46. f (x) 5 5x 2 2, g(x) 5 x 1 2 }5f ( g (x)) 5 5 1 x 1 2 }5 2 2 2 5 x 1 2 2 2 5 x(5x 2 2) 1 2g ( f (x)) 5 }55 5x }5 5 xBecause f ( g(x)) 5 x and g ( f (x)) 5 x, f and g are inversefunctions.47. f (x) 5 23x 1 10, g (x) 5 10 2 x }3f ( g (x)) 5 23 1 10 2 x }3 2 1 10 5 210 1 x 1 10 5 x10 2 (23x 1 10) 10 1 3x 2 10g ( f (x)) 5 }} 5 }}335 3x }3 5 xBecause f ( g (x)) 5 x and g ( f (x)) 5 x, f and g are inversefunctions.48. f (x) 5 4x 3 2 7, g(x) 5 1 }x 1 74 2 1/3f ( g (x)) 5 4 1 1 }x 1 74 2 1/3 2 3 2 7 5 41 }x 1 75 x 1 7 2 7 5 x4 2 2 7g ( f (x)) 5 1 (4x3 2 7) 1 7 1/3}}42 5 1 }4x342 1/3 5 (x 3 ) 1/3 5 xBecause f ( g (x)) 5 x and g ( f (x)) 5 x, f and g are inversefunctions.49. f (x) 5 x5 1 7}, g (x) 5 5 12Ï } 12x 2 7( Ï 5} 12x 2 7 ) 5 1 7f ( g (x)) 5 }} 5 }12x 2 7 1 7 5 }12x1212 12 5 x5Î}}g ( f (x)) 5 121 x5 1 7}12 2 2 7 5 Ï 5 } x 5 1 7 2 7 5 Ï 5 } x 5 5 xBecause f ( g (x)) 5 x and g ( f (x)) 5 x, f and g are inversefunctions.7.8.9.1( 0,2 )21322(1, 0.18)f(x)1( 2 )f(x) 5 e 2x 1 13( 0,2 )(1, 1.18)( )1 xf(x) 5 e 2x2(1, 1.93)3( 0,2 )y 5 1.5e 0.25x 1211( 1, 22 )y 5 1.5e 0.25(x 2 1) 2 2X=5 Y=223.65901yxx(2, 20.07)Domain: all real numbersRange: y > 1Domain: all real numbersRange: y > 22Use the trace feature to determine that l ø 224when t 5 5.The length of a 5-year-old tiger shark is about224 centimeters.10. A 5 Pe rt where p 5 2500 and r 5 0.05a. When t 5 2: A 5 2500e 0.05(2) 5 2500e 0.1 ø 2762.93The balance after 2 years is $2762.93.b. When t 5 5: A 5 2500e 0.05(5) 5 2500e (0.25) ø 3210.06The balance after 5 years is $3210.06c. When t 5 7.5: A 5 2500e 0.05(7.5)5 2500e 0.375 ø 3637.48The balance after 7.5 years is $3637.48.Algebra 2Worked-Out Solution Key427