Problem 20.1

Let f, g : IR IR be the functions f(x) = 2x and g(x) = (2x3+2x)/(x2+1) . Show that f = g.

Problem 20.3

Find functions defined on the set of nonnegative integers that define the sequences whose first six terms are given below.

a. 1, 1/13, 1/5, 1/7, 1/9, 1/11

b. 0, 2, 4, 6, 8, 10.

Problem 20.5

Let = {a, b} and be the set of all strings over .

a. Define f : ZZ as follows:

f(s) = the number of b's to the left of thee leftmost a in s, 0 if s contains no a's

Find f(aba), f(bbab), and f(b). What is the range of f?

b. Define g : as follows:

g(s) = the string obtained by writing the characters of s in reverse order.

Find g(aba), g(bbab), and g(b). What is the range of g?