1. Consider the curve y = f(x) = 2* - 1. A. Find the exact area of the region in the first quadrant bounded by the curves y = f(x) = 2*1 and y=x. ("Exact area" means no calculator numbers.) B. Find the inverse function y = -¹(x). C. Using part A and the notion of symmetry between a function and its inverse, find the exact area of the region in the first quadrant bounded by the curves y=f(x) and y=x. Explain your reasoning. (Hint: Think "graphically" and little or no math will need to be done!) D. Find a value for a such that the average value of the function f(x) on the interval [0,a] is equal to 1. You may use a calculator here.

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