Composition of Functions

Information For questions 1 - 3, use the tables below to evaluate the composite functions. X f(x) X 9(x) -1 1 2 O 5 S 2 -2 N 6 -10 10 51 Question 1 g (f(0)) Not yet answered Select one: Points out of O a. 1 11.11 O b. 2 O c. 5 Od. 7 O e. 8Question 2 f(g (1) ) Not yet answered Select one: Points out of O a. 2 11.11 O b. 4 O c. 8 O d. 7 O e. -2 Question 3 fog(- 10) Not yet answered Select one: Points out of O a. 0 11.11 O b. 6 O c. 1 O d. 8 O e. -1Question 4 Let f(x) = x-5 and g(x) = -2x+3. Find the formula for g(f(x)). Not yet answered Select one: Points out of O a. -2x - 2 11.11 O b. -2x+ 13 O c. - x - 2 O d. - 2x2 + 13x-15 Question 5 Let g(n) = 3n +2 and f(n) = 2n2+5. Find g(f(2)). Not yet answered Select one: Points out of O a. 135 11.11 O b. 41 O c. 28 O d. 62Information For questions 6 - 7, let f(x) = Ixl, g(x) = (x-2)2-3, and h(x) = -x. Question 6 Find the formula for f(g (x)). Not yet answered Select one: Points out of O a. (x+2) 2+31 11.11 O b. |(x+ 2)2-31 O c. |(x-2)2-31 O d. ( x-2) 2 - 3 Question 7 Find the formula for h(g(x)). Not yet answered Select one: Points out of O a. [(x-2)2+3] 11.11 O b. [(x-2)2-3] O c. -[(x-2)2-3] O d. -[(x-2)2+3]Information For questions 8 - 9, let j(x) = x2+ 3, k(x) = Ixl, and m(x) = Vx. Question 8 Find the formula for m(j(x)). Not yet answered Select one: Points out of O a. Vx+3 11.11 O b. x2+3 O c. Vx+3 O d. x+3 Question 9 Find m(k(-4)). Not yet answered Select one or more: Points out of O a. -2 11.12 O b. 4 O c. 2 O d. -V2 O e. -4 Of. V2Question 1 A function g is the inverse of function f. The point (-6, 1) is on the graph of f. Which of the following points is on the graph of g? Not yet answered Select one: Points out of O a. (6, 1) 20.00 O b. (6, -1) O c. (1, 6) O d. (1, -6) O e. (-6, -1)Question 2 Not yet Gabriella is asked to show that the functions f(x) = 3x -5 and g(x) = x+5 3 are inverses. Her work is shown below. Does she answered receive full credit? Points out of 20.00 f(x) = 3x - 5 g(x) *+5 3 f(g(x)) = 3-5 =x+5-5 f(x) = 3x -5 and g(x) = *+5 3 - are inverses. Select one: O a. No. The functions fand g are inverses, but Gabriella must show that g(f(x)) equals x also. O b. No. The functions f and g are not inverses. O c. It cannot be determined whether the functions fand g are inverses without graphing paper. O d. Yes. Gabriella has shown that fand g are inverses.Information For questions 3 - 4, the graph of a function fis given. Graph the function and its inverse on the same coordinate system. Question 3 Not yet answered Points out of 20.00 Select one: O a. E\fQuestion 5 Given the function f(x) = 5x +1 find f-1 (x). Not yet answered Select one: Points out of 20.00 O a. f- 1 ( x ) = *- 1 5 O b. f-1 ( x ) = 5x- 1 O c. f - 1 ( x ) = - 1 5x + 1 O d. f-1 ( x ) = - =x+ 1Information For questions 1 - 6, evaluate each logarithm. Question 1 log2 32 Not yet answered Select one: Points out of 10.00 O a. -16 O b. - 5 O c. 5 O d. 8 O e. 16 Question 2 log64 8 Not yet answered Select one: Points out of 10.00 O a . 1 Ob. 1 2 O c. O d. -8 O e. 2Question 3 In e ? Not yet answered Select one: Points out of Oa. 7 10.00 Ob. er O c. 14 O d. 1 7 Oe. e Question 4 Not yet log 125 5 answered Points out of Select one: 10.00 O a. 3 O b. 1 3 O c. -3 O d. 25 O e. _ w / -Question 5 log- 1 Not yet answered Select one: Points out of 10.00 O a. 0 O b. -7 O c. 1 O d. 1 7 O e. 7 Question 6 Convert the exponent equation 73 = 343 to logarithmic form. Not yet answered Select one: Points out of O a. log, 343 = 3 10.00 O b. log3 343 =7 O c. log 37 = 343 O d. log, 3 = 343 O e. log3 7 = 343Information For questions 7 - 8, identify the argument of each logarithm. Then, determine the domain. Question 7 f(x) = 1096(x+1)-2 Not yet answered Select one: Points out of 10.00 O a. The argument is x + 1. The domain is (-1, 0). O b. The argument is x + 1. The domain is (6, co). O c. The argument is 6. The domain is (-1, co). O d. The argument is x + 1. The domain is (0, co). O e. The argument is 6. The domain is (1, co). Question 8 f(x) = log, (2x) Not yet answered Select one: Points out of 10.00 O a. The argument is 2x . The domain is (9, o). O b. The argument is 2x. The domain is (0, co). O c. The argument is 9 . The domain is (0, co). O d. The argument is 2x . The domain is (-2, co). O e. The argument is 9. The domain is (-2, co).Question 9 Which of the following represents the graph of the logarithmic function f(x) = log5(x -2)-3? Not yet answered Select one: Points out of 10.00 O a . O b. O c . E\fQuestion 10 An exponential function has a range of (2, ). Which of the following statements must be true. Not yet answered Select one: Points out of O a. The inverse of the exponential function is a logarithmic function with a range of (2, co). 10.00 O b. The inverse of the exponential function is an exponential function with a domain of (2, co). O c. The inverse of the exponential function is a logarithmic function with a domain of (-2, co). O d. The inverse of the exponential function is a logarithmic function with a domain of (2, o). O e. none of the aboveAssignment: Properties of Logarithms Directions: Use your knowledge of the properties of logarithms to answer the following questions. For questions 1 - 4, determine whether each statement is true or false. If a statement is false, explain why. log x 1 . = log log y 2. n . log x = log xn 3. log x + log y = log xy 4. log5 6 = log For questions 5 - 8, write each expression as a logarithm with a single argument. Simplify, where possible. 5. log 4x + log(2x + 4) 6. 5 log x + log x 7. 4 log2 X + - 1092 9 - 1092 y 8. 6 log3 Z2 + - 1093 8 - 2 log3 zayFor questions 9 10, evaluate each expression, Round decimals to four places, 1 9. log9 12+ Elog3 5 10. log2 3X log3 4 X log4 5