Problem 1 let fx 5x2 - 7x 8 and gx 1 - 3x a find the

Question

Problem 1: Let f(x) = 5x² - 7x + 8 and g(x) = 1 - 3x.

a. Find the difference function (f - g)(x) and simplify the result. Show work.

b. Find (g - f)(-1). Show work.

c. Find (fg)(-1). Show work.

Problem 2: The cost, in dollars, for a company to produce x widgets is given by C(x) = 4700 + 5.20x for x > 0, and the price-demand function, in dollar per widget, is p(x) = 40 - 0.02x for 0 < x < 2000.

a. Find and interpret C(500).

b. Find and interpret C(500). (Note that C(x) is average cost function.)