Question 1 (2 points) Amy and Betty want to nd the inverse function of f(x] = x 3. Amy thinks it is A (x) = and Betty thinks it is B(x) = x + 3. Write an argument convincing them of what the inverse function actually is and (+1 bonus} why one / both of them is getting confused. Question 2 (5 points) CREATE. Sketch graphs of the functions that satisfy the given conditions. Label carefully so it is clear your function has these properties. (+2 for each graph) (a). A(x) has domain [35], range [2.2] (b). B(x) has domain [oo,oo), range [2, co), and DOES have an inverse function. and DOES NOT have an inverse function. y Y (c). Justify your answers in (a) and (b). Question 3 (4 points) Use this table to evaluate the following expressions or explain why you can't. (a). (1 point) f(g(5}) = (b). (1 point) g(g(1)} = (c). (1 point) For g(x} = 0, x = (d). (1 point) Assume all values for f, g are shown by this table. Does f have an inverse function? Does g? Justify. Question 4 (4 points) You are getting ready to host a party and you have set aside a certain amount of money to split between purchasing food and purchasing decorations. The amount of money you spend (in $) to purchase food is a function, F, of the number of people, p, you expect at the party. The amount of money (in $) you have to spend on decorations is a function, D, of the amount money (in $) you spend on food, 3:. Assume both functions have inverse functions. For each of the following, if the expression makes sense then explain what it means in the context of the party otherwise explain why it does not make sense. Be as specific as possible in your explanation (include units, what does the input/ output represent, etc). (a). (1 point) F(D(20}) (b). (1 point) D(F(20)) (c). (1 point) F_1(12) (d). (1 point) D-1(20)