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) = 2x - 1 and y = x. ("Exact area" means no calculator numbers.) B. Find the inverse function y = f (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 = "(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 (x) on the interval [0,a] is equal to 1. You may use a calculator here.2. A particle moves on a coordinate line with an acceleration at time / seconds of ell2 misec2. At 1= 0 the particle is at the origin, and its velocity is -4 m/sec. A. Find a function v() that gives the velocity of the particle at time . B. At what (exact) time is the velocity of the particle 0 m/s? C. Set up an expression (which may contain integrals, but not absolute values) to find the total distance traveled by the particle from time ? = 0 to r = 6. You do not have to solve your expression. 3. A culture of bacteria is growing at a rate of 40-5 per hour, with : in hours and 0 s :