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Use the composition cancellation equations to verify that f and g are inverse functions f(x)-wx +7 +11, g(x)=(8271Y-7 Choose the correct answer below OA (fegMP 3(:/%!-1.11).7sx-7 27-7+7+11-3.3X-11) 27 O C. (fo g)x) -3 (3Â·?+7+11)-11 27 (fo g)(x) Choose the correct answer below 27??7|+7+11:3-31(x-11) 27 3-Vx+7+ 11) - 11 27 -7-x+7-7-y ? ?. TI +111-11-3.31(x-11) 7 11-x
Show transcribed image text Use the composition cancellation equations to verify that f and g are inverse functions f(x)-wx +7 +11, g(x)=(8271Y-7 Choose the correct answer below OA (fegMP 3(:/%!-1.11).7sx-7 27-7+7+11-3.3X-11) 27 O C. (fo g)x) -3 (3Â·?+7+11)-11 27 (fo g)(x) Choose the correct answer below 27??7|+7+11:3-31(x-11) 27 3-Vx+7+ 11) - 11 27 -7-x+7-7-y ? ?. TI +111-11-3.31(x-11) 7 11-x

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3 Oct 2019

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Algebra

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Given f(x) = 3x2 - 2 and g(x) = 3 - 1/2 x2: find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Simplify your answer.) find the following expressions, (f.g)(4) (g.f)(2) (f.f)(l) (g.g)(0) (fog)(4) = (Type an exact answer, using radicals as needed. Simplify your answer.) Given f(x) = |x| and g(x) =9/x2+3, find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Type an integer or a simplified fraction.) For the function on the right determine whether the function is one-to-one. Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes Find the inverse of the one-to-one function. State the domain and range of the inverse function. {(10,-8), (-13,-10), (-9,2), (-8,11), (-10,1)} Which of the following is the inverse function? {(-10,1), (-8,11), (-9,2), (-13,- 10), (10,-8)} {(-8,10), (-10,-13), (2,-9), (11,-8), (1,-10)} {(-8,-10), (-10,-8), (2,-9), (11,-13), (1,10)} {(-10,8), (13,10), (9,-2), (8,-11), (10,-1)} Consider the functions f(x) = - 3x + 7 and g(x) = -1/3(x - 7). Find f(g(x)). Find g(f(x)). Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Consider the functions f(x) = 3x - 15 and g(x) = x/3 + 5. Find f(g(x)). Find g(f(x)) Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Match the graph to one of the following functions. y = 6x y = 6-x y = -6x y = -6-x y = 6x_ 1 y = 6x-1 Which function is represented by the graph? (Type A, B, C, D, E, F, G, or H.) Begin with the graph of y = ex and use transformations to graph the following function. Determine the domain, range, and horizontal asymptote of die function. f(x) = 8e-x Choose the correct graph below. Solve the equation. 4x.2x2=162 x = (Use a comma to separate answers as needed.) If 4-x = 5;what does 42x equal? 42x = (Type a reduced fraction.)

Show transcribed image text Given f(x) = 3x2 - 2 and g(x) = 3 - 1/2 x2: find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Simplify your answer.) find the following expressions, (f.g)(4) (g.f)(2) (f.f)(l) (g.g)(0) (fog)(4) = (Type an exact answer, using radicals as needed. Simplify your answer.) Given f(x) = |x| and g(x) =9/x2+3, find the following expressions. (f.g)(4) (g f)(2) (f.f)(l) (g.g)(0) (f . g)(4) = (Type an integer or a simplified fraction.) For the function on the right determine whether the function is one-to-one. Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No For the function below, determine whether the function is one-to-one. {(7,7),(8,8),(9,46),(10,51)} Is the function one-to-one? Yes No The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Is f one-to-one? Choose the correct answer below. No Yes Find the inverse of the one-to-one function. State the domain and range of the inverse function. {(10,-8), (-13,-10), (-9,2), (-8,11), (-10,1)} Which of the following is the inverse function? {(-10,1), (-8,11), (-9,2), (-13,- 10), (10,-8)} {(-8,10), (-10,-13), (2,-9), (11,-8), (1,-10)} {(-8,-10), (-10,-8), (2,-9), (11,-13), (1,10)} {(-10,8), (13,10), (9,-2), (8,-11), (10,-1)} Consider the functions f(x) = - 3x + 7 and g(x) = -1/3(x - 7). Find f(g(x)). Find g(f(x)). Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Consider the functions f(x) = 3x - 15 and g(x) = x/3 + 5. Find f(g(x)). Find g(f(x)) Determine whether the functions f and g are inverses of each other. What is f(g(x))? f(g(x)) = (Simplify your answer.) Match the graph to one of the following functions. y = 6x y = 6-x y = -6x y = -6-x y = 6x_ 1 y = 6x-1 Which function is represented by the graph? (Type A, B, C, D, E, F, G, or H.) Begin with the graph of y = ex and use transformations to graph the following function. Determine the domain, range, and horizontal asymptote of die function. f(x) = 8e-x Choose the correct graph below. Solve the equation. 4x.2x2=162 x = (Use a comma to separate answers as needed.) If 4-x = 5;what does 42x equal? 42x = (Type a reduced fraction.)

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Algebra

Which rational function has the given graph? R(x) = 2x2/x2-4 R(x) = 2x2/x2+4 R(x) = -2x2/x2+4 R(x) = 2x2/x2+4 (R(x) = -2x2/x2-4 Use a transformation of the graph of y = x5 to graph the function. h(x) = -4x5 Choose the correct graph below. Determine whether the function is a polynomial function. If it is, state the degree. If it is not tell why not. g(x)= 1-x3/5 Choose the correct answer below. Polynomial of degree 3 Not a polynomial because of the negative coefficient of x3 Polynomial of degree 1 Not a polynomial because of the negative power of x Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 27/x2-x-6 Find the vertical asymptote(s), it any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the horizontal asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no horizontal asymptote. Find the oblique asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) . There is no oblique asymptote. Use a transformation of the graph of y= x4 to graph the function. f(x) = (x+7)4 Find the vertical, horizontal and oblique asymptotes, if any, for the following rational function. R(x) = 8x/x+16 Select the correct choice below and till m any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Which rational function could have the given graph? In the functions shown, c is a constant. Choose the correct answer below. R(x) = (x+1)2(x+4)(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 R(x) = (x+1)(x+4)2(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 Analyze the graph of the function. R(x) = x(x-9)2/(x+12)3 What is the domain of R(x)? {x|x 0, x 9, and x - 12} {x|x -12} {x|x 0 and x - 12} All real numbers What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. x= (Use a comma to separate answers as needed. Type an integer or a fraction.) There is no vertical asymptote. What is the equation of the horizontal or oblique asymptote of R(x)? Select the correct choice below and fill in any answer boxes within your choice. y = (Simplify your answer.) There is no horizontal or oblique asymptote. Choose the correct graph for R(x) below. Find the vertical horizontal and oblique asymptotes, if any, for the following rational function. T(x) = x3/x4 - 1 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y= . (Use a comma to separate answers as needed.) There is no oblique asymptote.

Show transcribed image text Which rational function has the given graph? R(x) = 2x2/x2-4 R(x) = 2x2/x2+4 R(x) = -2x2/x2+4 R(x) = 2x2/x2+4 (R(x) = -2x2/x2-4 Use a transformation of the graph of y = x5 to graph the function. h(x) = -4x5 Choose the correct graph below. Determine whether the function is a polynomial function. If it is, state the degree. If it is not tell why not. g(x)= 1-x3/5 Choose the correct answer below. Polynomial of degree 3 Not a polynomial because of the negative coefficient of x3 Polynomial of degree 1 Not a polynomial because of the negative power of x Find the vertical, horizontal and oblique asymptotes, if any, of the given rational function. R(x) = x3 - 27/x2-x-6 Find the vertical asymptote(s), it any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Simplify your answer. Use a comma to separate answers as needed.) There is no vertical asymptote. Find the horizontal asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) There is no horizontal asymptote. Find the oblique asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Simplify your answer. Use a comma to separate answers as needed.) . There is no oblique asymptote. Use a transformation of the graph of y= x4 to graph the function. f(x) = (x+7)4 Find the vertical, horizontal and oblique asymptotes, if any, for the following rational function. R(x) = 8x/x+16 Select the correct choice below and till m any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no oblique asymptote. Which rational function could have the given graph? In the functions shown, c is a constant. Choose the correct answer below. R(x) = (x+1)2(x+4)(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 R(x) = (x+1)(x+4)2(x+c)/(x-1)(x+3) R(x) = (x+1)(x+4)(x2+c)/(x-1)2(x+3)2 Analyze the graph of the function. R(x) = x(x-9)2/(x+12)3 What is the domain of R(x)? {x|x 0, x 9, and x - 12} {x|x -12} {x|x 0 and x - 12} All real numbers What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. x= (Use a comma to separate answers as needed. Type an integer or a fraction.) There is no vertical asymptote. What is the equation of the horizontal or oblique asymptote of R(x)? Select the correct choice below and fill in any answer boxes within your choice. y = (Simplify your answer.) There is no horizontal or oblique asymptote. Choose the correct graph for R(x) below. Find the vertical horizontal and oblique asymptotes, if any, for the following rational function. T(x) = x3/x4 - 1 Select the correct choice below and fill in any answer boxes within your choice. The vertical asymptote(s) is/are x = . (Use a comma to separate answers as needed.) There is no vertical asymptote. Select the correct choice below and fill in any answer boxes within your choice. The horizontal asymptote(s) is/are y = . (Use a comma to separate answers as needed.) There is no horizontal asymptote. Select the correct choice below and fill in any answer boxes within your choice. The oblique asymptote(s) is/are y= . (Use a comma to separate answers as needed.) There is no oblique asymptote.

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