Hello please help with the following questions by showing ALL CALCULATIONS IN TEXT if possible. Also, this is not for an assignment but rather merely for my understanding and comprehension. Thank you.

1) Let f (x)= log?(x) +3 and g(x) = log?(x)-1.

• Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form.
• Part B: Determine the solution to the system of nonlinear equations.

2) 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) =-2x + 13x + 7, where represents the distance from the coach. The path of the second player's ball can be represented by the function h(x) = -x+ 4x + 21.

• Part A: Find the distances in which the two basketball paths will cross. Show all necessary calculations.
• Part B: Let g(x)/h(x); Solve for f (x) in simplest form and determine all discontinuities.

3) Let y =2(x-5)-6.

• Part A: Is the given relation a function? Is it one-to-one? Explain completely. If it is not one-to-one, determine restriction on the domain such that the relation is one-to-one.
• Part B: Determine y?. Show all necessary calculations.
• Part C: Prove algebraically that y and y ? are inverse functions.

4) An interior designer wants to decorate a newly constructed house. The function f (x) = 36x-150 represents the amount of money he earns per room decorated, where x represents the number of rooms he designs. The function g(x)=1/6X 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.
• Part B: If the newly constructed house requires 45 hours of work, how much will the interior designer earn? Show all necessary calculations.
• Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work.

5) A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 16 mm halfway across a horizontal distance of 80 mm.

• Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work.
• Part B: Identify the focus, directrix, and axis of symmetry of the parabola.

(ac, y) C (a, b) b X