1 Given f = { (-1, 8), (3, -1), (-2, 0) } and g = { (-5, 8), (3, -1), (-1, 0) } . Find (f o g)(3). Show steps,

2 Given f = { (-1, 8), (3, -1), (-2, 0) } and g = { (-5, 8), (3, -1), (-1, 0) } . Find (g o f)(3). Show steps,

3 Given f (x) = 2x + 3 and g(x) = -x² + 5. . Find (f o g)(1). Show steps.

4 The f and g functions are the same in Ex. 4 and #3 above. Is the answer the same? Why or why not?

B With the given functions, find the composition requested. Show your work as it is done in the lesson content. (See Exs. 4-6..)

5 f(x) = 15x -12 and g(x) = -15x² + 14x - 10, find (f o g)(-1).

6 f(x) = -13x² -13x + 14 and g(x) = -13x - 11, find (g(g(-3)).

C Find the composition of functions defined andstate the domain of the composite function showing your work. (See Ex. 7)

7 f(x) = 2x + 3 andg(x) = -x² + 5, find (g o g)(x).

8 f(x) = x + 3 and g(x) = x, find g(f(x)).

9 f(x) = x - 1 and g(x) = 3/(x-1), find f(g(x)).

D Apply Your Knowledge (See Ex. 8.)

10 You go to a local mechanic to get your tires changed. The tires cost x dollars. There is a 6% sales tax, but you get a 10% discount.

A What is the function t(x) for the total purchase amount after taxes but before discounts and fees.

B What is the function d(x) for the total after discounts on purchase amount x but before taxes and fees.

C Does it make a difference in the total price whether the mechanic adds the tax first d(t(x)) or takes the discount first t(d(x))? Do not replace x with a numerical value. Show the work to support your answer while keeping x in your work.