Chapter 12 and 13 Math 125 Practice set Note: the actual test differs. Given f(x) and g(x), find the indicated composition and

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1 Chapter 1 and 13 Math 1 Practice set Note: the actual test differs. Given f() and g(), find the indicated composition. 1) f() = - ; g() = 3 + Find (f g)(). Determine whether the function is one-to-one. If so, find a formula for the inverse. 8) h() = 3-1 ) f() = + ; g() = 9 + Find (g f)(). 3) f() = + 8; g() = + 8 Find (f g)(). Given f() and g(), find the indicated composition and evaluate. ) f() = 3 + 6; g() = Find (g f)(3). ) f() = ; g() = - 1 Find (f g)(11). Determine whether the function is one-to-one. If so, find a formula for the inverse. 9) g() = - 3 ) g() = Determine whether the function is one-to-one. Give a valid reason. 6) f() = 6-6 For and 6 Determine whether the function is one-to-one. If so, find a formula for the inverse. 11) h() = Determine whether the function is one-to-one. Give valid reason. 7) f () f Determine whether the function is one-to-one. If so, find a formula for the inverse. 1) f() = - 9 Graph the function using a solid line and its inverse using a dashed line on the same set of aes. 13) f() =

2 1) f() = + Graph. 18) = ( + 1) For the function f, use composition of functions to show that f -1 is as given. 1) Let f() = + 3. Show that f-1 = ) Let f() = 3 -. Show that f -1 () = 3 +. Graph. Label at least two points on each graph. 17) = Solve the problem. 19) The amount of particulate matter left in solution during a filtering process decreases Simplif. b the equation P = 600 (0.). 6 n, where n is the number of filtering steps. Find the amounts left for n = 0 and n =. (Round to the nearest whole number.) 0) log 1 1) log 1 ) log 8 3 3) log 0.01 ) log 6 6 ) log 6) log 8 1

3 Graph. 7) = log 3) z = 8 Solve the problem. 36) log 8 = 37) log = ) log 1 = 39) log = -3 Graph. Label at least two points on the graph. 8) = log 1/ ) log 6 = 3 Epress as a sum of logarithms. 1) log 6 () ) log (z) Epress as a single logarithm. 3) log log 6 1 ) log 11 + log 1 Rewrite as an equivalent eponential equation. Do not solve. 9) log = Epress as a product. ) log 7 9 6) log c Z - 30) log 6 36 = 31) log = - 3) log = Rewrite as an equivalent logarithmic equation. Do not solve. 33) 3 = 8 3) 83,3 1/7 = 7 Epress as a difference of logarithms. 7) log g M 67 Epress as a sum, difference, and product of logarithms, without using eponents. 8) log 1 13 r s 9) log b m p 8 n 9 b 3

4 Epress as a single logarithm, and, if possible, simplif. Simplif. 0) loga + 1 log a z 1) 1 log a + 6 loga - loga ) 1 log a + loga - 3 loga 3) logw ( - 6) - logw ( - 8) ) log a a 09 ) log e e Solve. Where appropriate, include approimations to the nearest thousandth. If no solution eists, state this. 6) ( - ) = 6 7) 8 = 16 ( + ) 8) = 6 9) 9 = 81 ( + 9) 60) log = 1 Solve the problem. 66) Yearl sales of an electronic device S(t), in millions of dollars, t ears after 1997 can be estimated b S(t) = 00 t. What is the doubling time for the earl sales? 67) Find the hdrogen ion concentration of a solution whose ph is.6. Use the formula ph = -log [H + ]. 68) Suppose that $6000 is invested in an account where interest is compounded continuousl at 3.7% per ear. What is the balance after 1 ear? after ears? 69) Suppose that $7000 is invested in an account where interest is compounded continuousl at 3.% per ear. What is the doubling time? Solve. 70) How long will it take for the population of a certain countr to triple if its annual growth rate is 3. %? (Round to the nearest ear.) Choose the equation that matches the graph. 71) 61) log - log( + 7) = 1 6) log ( - 8) + log ( - 8) = ) ln - ln ( - 6) = ln 6) ln ( - 6) + ln ( + ) = ln 6) ln ( - ) + ln ( + ) = ln 36 - A) ( - 1) + ( - ) = B) ( - 1) - ( - ) = 16 C) ( - 1) + ( - ) = D) ( - 1) + ( - ) = 16

5 Graph. Be sure to label the verte. Round to the nearest hundredth if necessar. 7) = - 7) = Graph. Be sure to label the verte and at least one other point on the graph. Find an equation of the circle satisfing the given conditions. 76) Center at (, 7), radius 6 77) Endpoints of a diameter: (, -) and (, 1) 73) = 1 Graph. Label the intercepts. 78) + 9 = Graph. Be sure to label the verte. Round to the nearest hundredth if necessar. 7) = - Graph. 79) + 6 =

6 80) = ) 9( - ) + ( + 1) = 8) 6-1 = 1 A) A horizontal ellipse. B) A hperbola with a horizontal ais C) A hperbola with a vertical ais. D) A vertical ellipse. 86) ( - 7) + ( + 1) = A) A circle with its center at the origin. B) An ellipse with its center at the origin. C) A circle with its center not at the origin. D) An ellipse with its center not at the origin. 87) - = A) A parabola opening to the right or left. B) A vertical ellipse. C) A hperbola with a vertical ais. D) A parabola opening upward or downward Find the equation in standard form of an ellipse centered at the origin that passes through the given points. 8) (-, 0), (, 0), (0, -9), and (0, 9) 88) ( - ) + ( + ) 16 = 1 A) A circle with its center not at the origin. B) A hperbola with its center not at the origin. C) An ellipse with its center not at the origin. D) A parabola with its center not at the origin. 83) (-3, 0), (3, 0), (0, - ), and (0, ) Choose the description that matches the equation of the conic section. 8) 6-36 = 1 A) A hperbola with a horizontal ais. B) A horizontal ellipse. C) A hperbola with a vertical ais. D) A vertical ellipse. Graph. Label the intercepts 89) 36 - =

7 Graph. 90) 16 - = 6 9) - = 1 9) 16 = ) = ) 9-6 = 18 97) = 6 Find the vertices of the hperbola. 98) - 36 = 900 Find the asmptotes of the hperbola. 99) - 00 = 1 Solve. 0) + = 1 - = ) = - - 1) + = 0 - = ) - = -0 - = 3 3) + + = 0 + = 3 ) - = 1 = 3 ) + - = = ) + = 36 - = 36 Classif the following as the equation of a parabola, a circle, an ellipse, or a hperbola. 93) + = 7

8 Answer Ke Testname: 1CH1&13P 1) (f g)() = ) (g f)() = ) (f g)() = + 16 ) 1 ) 30 6) No 7) Yes 8) h -1 () = ) Not a one-to-one function ) g -1 () = ) h -1 () = 3-7 1) f -1 () = + 9, 0 13) ) ) 1. (f -1 f)() = f -1 (f()) = f (f f -1 )() = f(f -1 ()) = f(3 - ) = = (3 - ) = ( + ) - = ; = 3 3 = 8

9 Answer Ke Testname: 1CH1&13P 16) 1. (f -1 f)() = f -1 (f()) = f -1 ( 3 - ) = 3 ( 3 - ) + = 3 3 = ;. (f f -1 )() = f(f -1 ()) = f( 3 + ) = 17) = + - = ) ) 600, 7 0) -1 1) - ) 3 3) - ) ) 6) 3 9

10 Answer Ke Testname: 1CH1&13P 7) ) ) = 30) 6 = 36 31) 3 - = 1 9 3) = 33) 3 = log 8 3) 1 7 = log 83,3 7 3) z = log 8 36) 3 37) 38) ) 1 0) 16 1) log 6 + log 6 ) log + log + log z 3) log 6 1 ) log 13

11 Answer Ke Testname: 1CH1&13P ) 9 log 7 6) - log c Z 7) log g M - log g 67 8) log log 1 r - log 1 s 9) log b m + 8log b p - 9log b n - 0) loga ( z 1/ ) 1) loga 6 7/ ) loga / 3) logw ( + 8) ) 09 ) 6) 7) - 8 8) -3, 1 9) No solution 60) 61) No solution 6) 63) 1 6) 9 6) 7 66) 1.0 r 67) ) $66.16; $ ) 0. r 70) 3 ears 71) D 7) (0, 0)

12 Answer Ke Testname: 1CH1&13P 73) (0, 0) ) (-, 0) ) - 6., ) ) ( - ) + ( - 7) = 6 77) = 1

13 Answer Ke Testname: 1CH1&13P 78) 79) )

14 Answer Ke Testname: 1CH1&13P 81) ) = 1 83) 18 + = 1 8) A 8) C 86) C 87) D 88) C 89)

15 Answer Ke Testname: 1CH1&13P 90) ) ) ) Circle 9) Parabola 9) Hperbola 96) Circle 97) Hperbola 98) (0, 6), (0, -6) 99) = 3, = - 3 0) (9, 8), (-8, -9) 1

16 Answer Ke Testname: 1CH1&13P 1) (0, ), (-,0) ) (, 1) and -8, ) (0,0) 300 9, ) (3, 1), (-3, -1) ) (9, 3), (-9, 3), (3, 9), (-3, 9) 6) (6, 0) and (-6, 0) 16

Math125 Exam 5 Review Name. Do the following as indicated.

Math125 Exam 5 Review Name. Do the following as indicated. Math Eam Review Name Do the following as indicated. For the given functions f and g, find the requested function. ) f() = - 6; g() = 9 Find (f - g)(). ) ) f() = 33 + ; g() = - Find (f g)(). 3) f() = ;