Let y = 2(x - 4)2 - 8. Part A: Is the given relation a function? Is it one-to-one? Explain completely. If it is not one-to-one, determine a possible restriction on the domain such that the relation is one-to-one. (5 points) Part B: Determine y". Show all necessary calculations. (5 points) Part C: Prove algebraically that y and y are inverse functions. (5 points)An interior designer wants to decorate a newly constructed house. The function f (x) = 49x - 200 represents the amount of money he earns per room decorated, where x represents the number of rooms he designs. The function g(X ) = _ x represents the number of rooms the interior designer decorates, where x is the number of hours he works. Part A: Determine the amount of money the interior designer will make decorating the house as a function of hours he works. (5 points) Part B: If the newly constructed house requires 50 hours of work, how much will the interior designer earn? Show all necessary calculations. (5 points) Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work. (5 points)