CSC 300: Assignment 5
Due: Feb-20-08, in class
1. (4X3 pts) Determine whether each of these functions from {a,b,c,d} to itself is
a) one to one
b) onto
•f(a)=b, f(b)=a, f(c)=c, f(d)=d
•f(a)=b, f(b)=b, f(c)=d, f(d)=c
•f(a)=d, f(b)=b, f(c)=c, f(d)=d
2. (2X3 pts) Determine whether f is a function from Z (set of integers) to R (set of real numbers)
a)
fn=±n
b)
fn=
n21
c)
fn=1/n2−4
3. (3 pts) If
fx=2x−3
and
gy=3−5/y2
then what is the composition of g and f,
g(f(x)) ?
4. (5 pts) Write the pseudo-code of an algorithm that returns the sum of all integers in a list of
integers. You may use the Pascal-like pseudo-code notation in the textbook, or the C-like
notation I used in class, or any reasonable notation of your own, as long as you use its
components consistently.
5. (4 pts; Extra credits) Argue why the function
fx=ex
from the set R to R is not invertible
(i.e., its inverse does not exist), but it turns invertible if the co-domain is restricted to the set of
positive real numbers, R+