An interior designer wants to decorate a newly constructed house. The function f(x) = 36x-150 represents the amount of money he ears per room decoratedwhere

An interior designer wants to decorate a newly constructed house. The function f(x) = 36x²-150 represents the amount of money he ears per room decoratedwhere 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 thenumber 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 45 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)