Answering questions 1-20

For the given functions f and g, find the requested composite function. 1) f(x) = 4x2 + 4x + 6, g(x) = 4x - 3: Find (g of)(x). Find functions f and g so that f ag = H. 2) H(x) = VX +1 2) The function f is one-to-one. Find its inverse. 3) f(x) = 5x2 + 3, x20 3) A) -1(x) =3 B) f-1(x) = -*3 C) f-1(x) = _ Use transformations to graph the function. Determine the domain, range, and any asymptote of the function. 4) f(x) = -2X+3 + 4 4) 10 Write as the sum and/or difference of logarithms. Express powers as factors. 5) In (8x) 1+3x X > 6 5 ) (x - 6 ) 5 A) In 8 + In x + -In (1 + 3x) - 5In (x - 6) B) 8Inx + In (1 + 3x) - 5In (x - 6) C) In 8 + In x - 7In (1 + 3x) - 5In (X - 6) D) In 8 + In x + =In (1 + 3x) - In 5 - In (x - 6) Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. 6) log 5 76.4 6) Solve the equation. 7) log 3 (x - 5) + log 3 (x - 11) = 3 7) A) (2] B) (14} C) (15} D) (14. 2) 8) log (3x) = log 4 + log (x - 3) 8) Graph the function. Determine the domain, range, and horizontal asymptote of the function. 9) f(x) = 2 - In(x + 4) 9 ) -10 Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. 10) In x + In (x + 5) = -3 10) A) -5 - V25 + 4e-3 2 #-5.010 B) -5 + 125 + 4e-3 =0.020 C) -5 + V25 + 40-3 =0.010 D) -5 + 2\/25 + 0-3 2.505 Solve the equation. 11) 16% - 3 = 83x 11) 12) 3 - 521 - 1 = 75 12) Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. 3) 5 =31 - x 13) Solve the problem. 14) Find out how long it takes a $2900 investment to double if it is invested at 7% compounded 14 ) semiannually. Round to the nearest tenth of a year. Use the formula A - P( 1 + Ijnit A) 9.9 yr B) 10.1 yr C) 10.3 yr D) 10.5 yr 15) A culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present 15) initially and there are 609,000 after 6 hours, how long will it take for the population to reach one million 16) The logistic growth model P(1) = 210 1 + 34e-0.194t represents the population of a species introduced 16) into a new territory after t years. What will the population be in 20 years? A) 210 B) 133 C) 123 D) 29 17) The half-life of silicon-32 is 710 years. If 70 grams is present now, how much will be present in 400 17) years? (Round your answer to three decimal places.) A) 1.41 B) 47.37 C) D) 67.319 18) A wheel of radius 2.8 feet is moving forward at 17 feet per second. How fast is the wheel 18) rotating? Find the exact value of the expression. Do not use a calculator. 19) tan-1 tan 3m 19) A) 214 c) - ST D) - 27 20) cos-1 cos - 35 20) A) - B) - 21 C)