Question 1 [Essay Worth it] points) {e2.e2. 2:23 He} Let rtx} = logger} + 2 and gm = loggij 4. Perth: If her} = rm + gm, solve for mm in simplest term. {4 points] Part B: Determine the solution to the system of nonlinear equations. {6 points} Part 2(Essay Worth 10 points) (02.02, 2.03 HC) While warming up for a game, two basketball players shoot balls in parabolic paths. The path of the first 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) = -x~ + 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) = g(x) h(x ) Solve for f (x) in simplest form and determine all discontinuities. (6 points)Part 3 (Essay Worth 15 points) (02.06 HC) 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-1. Show all necessary calculations. (5 points) Part C: Prove algebraically that y and y are inverse functions. (5 points)