Schaum's Outline of Theory and Problems of Beginning Calculus

CHAP. 71FUNCTIONS AND THEIR GRAPHStYT'-2 -1 0w1 2 XI1tYXFig. 7-16(4x2 - 16ifx# -47.13 (a) Letf(x) = x - 4 and let g(x) = . Determine k so that f(x) = g(x) for all x.ifx= -4XL - x(b) Let f(4 = 7 g(x) = x - 1Why is it wrong to assert thatfand g are the same function?7.14 In each of the following cases, define a function having the given set 9 as its domain and the given set 9 asits range: (a) 9 = (0, 1) and 9 = (0, 2); (b) 9 = [0, 1) and 41 = [- 1, 4); (c) 9 = [0, 00) and 9 = (0, 1);(6) 9 = (-CO, 1) U (1,2) [that is, (-CO, 1) together with (1,2)] and 41 = (1, CO).7.15 For each of the functions in Problem 7.8, determine whether the graph of the function is symmetric withrespect to the x-axis, the y-axis, the origin, or none of these.7.16 For each of the functions in Problem 7.8, determine whether the function is even, odd, or neither even norodd.7.17 (a) Iffis an even function andf(0) is defined, mustf(0) = O?(b) Iffis an odd function andf(0) is defined, mustf(0) = O?(c) Iff(x) = x2 + kx + 1 for all x and iffis an even function, find k.(d) Iff(x) = x3 - (k - 2)x2 + 2x for all x and iffis an odd function, find k.(e) Is there a functionfwhich is both even and odd?7.18 Evaluate the expression f(x + h,hfor the following functions$