MODULE FIVE PROBLEM SET
This document is proprietary to Southern New Hampshire University. It and
the problems within may not be posted on any non-SNHU website.
TESTBANKSNERD
1
, Directions: Type your solutions into this document and be sure to show all steps
for arriving at your solution. Just giving a final number may not receive full credit.
PROBLEM 1
Indicate whether the two functions are equal. If the two functions are not equal,
then give an element of the domain on which the two functions have different values.
(a)
f : Z → Z, where f (x) = x2.
g : Z → Z, where g(x) = |x|2.
If we square an integer, an non negative result is obtained.
Considering
x2 = |x|2 for allx ∈ Z
Hence both functions are equal.
(b)
f : Z × Z → Z, where f (x, y) = |x + y|.
g : Z × Z → Z, where g(x, y) = |x| + |y|.
Let us say x and y have the same sign
f (x, y) = |x + y| = |x| + |y| = g(x, y)
But if x and y have opposite signs
f (x, y) /= g(x, y)
If x = -1, y = 1
Then
f (−1, 1) = | − 1 + 1| = |0| = 0
And
g(−1, 1) = | − 1| + |1| = 1 + 1 = 2
Therefore, the two functions are not equal.
This document is proprietary to Southern New Hampshire University. It and
the problems within may not be posted on any non-SNHU website.
TESTBANKSNERD
1
, Directions: Type your solutions into this document and be sure to show all steps
for arriving at your solution. Just giving a final number may not receive full credit.
PROBLEM 1
Indicate whether the two functions are equal. If the two functions are not equal,
then give an element of the domain on which the two functions have different values.
(a)
f : Z → Z, where f (x) = x2.
g : Z → Z, where g(x) = |x|2.
If we square an integer, an non negative result is obtained.
Considering
x2 = |x|2 for allx ∈ Z
Hence both functions are equal.
(b)
f : Z × Z → Z, where f (x, y) = |x + y|.
g : Z × Z → Z, where g(x, y) = |x| + |y|.
Let us say x and y have the same sign
f (x, y) = |x + y| = |x| + |y| = g(x, y)
But if x and y have opposite signs
f (x, y) /= g(x, y)
If x = -1, y = 1
Then
f (−1, 1) = | − 1 + 1| = |0| = 0
And
g(−1, 1) = | − 1| + |1| = 1 + 1 = 2
Therefore, the two functions are not equal.
