COMPLETE ALL. THEY MUST HAVE STEP BY STEP WITH EXPLANATIONS.

ORIGINAL ANSWERS

I WILL GIVE GOOD OR BAD FEEDBACK BASED ON THE FINAL SCORE. SO PLEASE TUTORS DO YOUR BEST, I NEED EXPERTS ON CALCULUS HERE, TAKE YOUR TIME BUT DO IT EXCELLENT. THANK YOU

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 g(x) = 2x2 + 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 + 4x + 12. Part A: Find the distances in which the two basketball paths will cross. Show all necessary calculations. (4 points) Part B: Let F(x) - %. Solve for fix) 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 Part B: Determine y"1. 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) - gx 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 destgner 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)