PLEASE ANSWER ALL QUESTIONS WITH A WHOLE EXPLANATION

Let f (x) = log2(x) + 2 and g(x) = log2(x3) - 6. Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points) Part B: Determine the solution to the system of nonlinear equations. (6 points)While warming up for a game, two basketball players shoot balls in parabolic paths, The path of the rst player's ball can be represented by the function 90:) : 723(2 + 11X + 6' where x represents the distance from the coach, The path of the second player's ball can be represented by the function h(x) : x2 + 4)! + 12, Part A: Find the distanoes in which the two basketball paths will cross, Show all necessary calculations (4 points) ) Part B: Let t'(x) -%, Solve for for) in Simplest form and determine all discontinuities. (6 points) 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 y1. 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) = 25x2 - 100 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 40 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)