Can you please answer the questions clearly ?

4 6 (a) Show that, for x # - 2. x42 =X-2. b) Are the functions f(x) and g(x) equal? Show that the function y = 19 can be written in the form y = ex. where it is a positive Let f(x) = 2 x20. Complete parts (a) through (c) below. constant. Determine H. X5 -4 ((x ) = *+2. *# - 2 g(x) =x-2. XER (a) Use a graphing calculator to graph f(x). Choose the correct graph below. All graphs have What is an appropriate formula, relationship, or property that can be used to transform the expression 79 into an expression of the form e" MX? OA. (a) Factor the numerator of the rational expression. The factored form of the nume rator is (x + 2)(x - 2) A. The property of logarithms, log as' =rlog as From the factored form of the numerator, it can be seen that dividing the numerator and B. The change of base formula, a* = exIna denominator by (x + 2) results in the expression x - 2. O c. The relationship xponential and logarithmic function, log a a* = x Select the correct choice below and, if necessary, fill in the oxes within your O D. The property of logarithms, log a(st) = log as + log at (Use a comma to separate answers as needed.) O A. Yes, because f(x) and g(x) have the same values for all values of x. Using the result found in the previous step, the expression | 79 | can be written in the form O B. No, because on the interval . g(x) = while f(x) is undefined. x In 1) O C. No, because on the interval . f(x)= while g(x) is undefined. (Use integers or fractions for any numbers in the expression. Do not simplify.) on the basis of the graph in (8), find the range of ((x). O D. No, because when x = . 9(x) = while f(x) is undefined Note that 79 can be written in the form 19 - 1 The range is O E. No, because on the interval . f(x)= while g(x) = (Type an integer or a decimal.) Simplify your answer. Type your answer in interval notation.) OF. No, because when x = , f(x) = while g(x) is undefined. Thus. = (In (19)) * by the property of logarithms that states that O G. No, because when x = . f(x) = while g(x) = log as' =rlog as. Suppose that f(x) =x2. x20, and g(x) = \\x. x20. Typically, fog#gef, but this is an Therefore. 79 can be written in the form e"MX where , = . which is a example in which the order of composition does not matter. Show that fog= gof. positive constant, as required. (a) Graph f(x) = x2. x20, and g(x) = x3, x20, together in one coordinate system. ( b) Show algebraically that x z x2 for Osx5 1 . (c) Show algebraically that x 5x2 for x 2 1. Which of the following is equivalent to (f o g)(x)? O A. 9["(x ) B. [g(x)] a) Graph the functions. Choose the correct graph below. All graphs have a window size of -10,10,1] by [- 10,10.1). O c. f(x) . 9(x) OD. ((x)+ 9(x) O B. Set up the composite function for (f o g)(x). Select the correct choice below and fill in the O A. y= 9[(x)]= 9( ) B. y= (19(x)]=(Vx ) Which of the following is equivalent to (g o f)(x)? S O A. f(x) + 9(x) OB. f(x) . 9(x) O C. f[g(x)] Let f(x) = x43 . *20. Complete parts (a) through (d) below. D. 9[f(x) Set up the composite function for (g of)(x). Select the correct choice below and fill in the answer box within your choice. (a) Use a graphing calculator to graph f(x). Choose the correct graph below. All graphs have a window size of [ - 10,10,1] by [ - 10,10,1]. ( Rewriting x 2 x2 as an inequality with 0 on one side results in the unfactored inequality O A. y= 19(x)] =( D 2 0. Factoring the left side results in 20. For all x on the interval 0 s xs1. OB. y= 9[1(X)] = 9 D O A. so the inequality is true, showing that 2x2 for 05x51. (3 (a) Show that y =x4, xEH, is an even function both factors are nonnegative , (b) Show that y = x , xER, is an odd function. both factors are negative ne factor is nonnegative and the other is negative, OC (a) A function f : A-B is called even if f(x) = f( -x) for all xEA. previous step. Let ((x) = x". Write the expression that corresponds to the right side of the equation in the (-x)* (Do not simplify.) Why is this expression equal to x4? b) Find the range of f(x). O A. Multiplying the base by itself four times results in a negative expression, which icels out the negative in front of the entire term. The range is 312 O B. Multiplying the base by itself any mes results in a positive expression (Simplify your answer. Type your answer in interval notation.) O C. Multiplying the base by itsel pression with the same sign as the base. (C) which values of x is f(x) = 7 D. Multiplying the base by itself four times results in a positive expression x = (b) A function f : A-+B is called odd if f(x) = -f(-x) for all xEA (Simplify your answer. Use a comma to separate answers is needed.) Let f(x) = x3. Write the expression that corresponds to the right side of the equation in the previous step (Do not simplify.)