24 Mathematical terms and notations Exercises Exercise 2.1 For each of the following functions f sketch the graph y = f (x) in R1. Decide whether the inverse function 1""1 exists, and if it does exist write down the formula for f'1(y). f(x) = 5x; f(x) = 3:2 4x + 8; f(x) = x5. Exercise 2.2 Each of the following definitions species a subset K ofRz. (In this question x is the name of the coordinate measured on the horizontal axis and y is the name of the coordinate measured on the vertical axis.) Hm) I 3x +4y = 12}, {(x, y) | 3x +4y g 12}, {(x, y) I x2 + y2 = 4}, {(xay) I x2 + y2 s 4}, {(m) I x2 = 4y}, {(m) I y2 = 4x}. In each case sketch the set K and indicate on your sketch the set K 0 R1. Exercise 2.3 Suppose that the supply and demand sets for a particular market are S ={(q,p) | 3pq=5}, D = {(qip) | 3p+qz+24=9}- Sketch S and D and determine the equilibrium set E = S n D. Comment briey on the interpretation of the results. Exercise 2.4 The functions f, g, h are given by f (x) = x2 + 1, g(x) = 1/x2, h(x) = J}. Find formulae for the compositions f g, g f , hf, f h, hf g. Exercise 2.5 Suppose that the supply and demand sets for a good are given by S = {(q,p) | 4 3p = 1}, D = {(q,p) | q H) = 2}- Determine the supply function, qs, the demand function, q\