Consider the functions f(z) = 8z 7 and g(z) = =i 1. 5. 6. Find and simplify the expression for (g o f) (a:) Show each step on a new line and line up equal signs. Start by writing (90 f)(z) = Find and simplify the expression for (f o g) (x) Show each step on a new line and line up equal signs. Start by writing (fog)(z) = Based on the results in #1 and #2, are f and g inverse functions of each other? Explain how what you found in #1 and #2 supports your answer to this question. Make a graph by following these steps: a. Go to https:/www.desmos.com/calculator. b. On the first line, enter the equation f(z) = 8z 7. c. On the second line, enter the equation g(z) = '\"'8\" . Try typing in x+7, then highlighting x+7 and then typing the "/" key. This should create an empty denominator for the 8. d. On the third line, enter the equation y = . e. Make sure everything can be seen in the window (zoom or move the window if needed). > f. Save a picture! You can either take a screen shot or click the - button in the upper right corner and export as an image. What is the visual relationship between the functions f and g with respect to the line y = z? Does your answer in #5 support or refute your answer in #3? Explain in complete sentences. 1. [3 points] Consider the two functions, m(x) = x-2 and p(x) = . Find and simplify the formula for (m . p) (x) and state its domain in interval notation. Domain of (m o p) (x) in interval notation: 2. [3 points] Use the table to evaluate the following or state it is undefined. X f(x) g (x) a.) f(-1) b.) 8(6) -1 7 5 2 2 0 c.) f(8(2) ) d.) (8.g)(-2) 3 0 -8 3 -2 4 -1 e.) f- (1) f.) 9 * (f (2) ) 1 6 2 6 1 -2MTHI 3. [3 points] Determine the equation for the inverse function of f(x) =; in explicit form x +7 (f- (x)=... ). Then state the domain of the inverse function in interval notation. Domain of f- in interval notation: 4. [1 point] The graph of the one-to-one function, g, is given. Draw the graph of the inverse function, g . Note the line y = x is drawn in for your convenience. -9 -8 -7 -6 -5 -4 -3 -2 -19 $3456 7 89