MATH213 HW 2
Due Wednesday, September 6
Solve five of the six problems below.
1. Find the domain and range of these functions.
a) the function that assigns to each real number its square;
b) the function that assigns to each positive real number the square root of it;
c) the function that assigns to each bit string the difference between the number of zero
bits and the number of one bits in this string;
d) the function that assigns to each pair of positive integers their sum.
2. Give an explicit formula for a function from the set of positive integers to the set of
non-negative integers that is
a) one-to-one, but not onto;
b) onto, but not one-to-one;
c) neither onto nor one-to-one;
d) both one-to-one and onto.
3. Let f(x) = 2x+ 1, g(x) = x2−2, and h(x) = x−10. Find
a) f◦g◦h, b) h◦g◦f, c) h◦g◦f◦h.
4. Draw the graphs of these functions.
a) f1(x) = bx+1
2c − 1; b) f2(x) = bx−1
3c+dx+1
3e;
c) f3(x) = b0.5d2x/3e+ 0.5c.
5. If we have pennies, dimes, quarters and dollars, but no nickels, does the greedy
algorithm always produce change using the fewest coins possible? If “yes”, give a proof, if
no, present a counterexample.
6. Problem 2 on page 129 of the book.