Snhu
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.
Neha Chandrahalli
snhu
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 :ZZ, where f(x)=x2 g:ZZ,where g(x)=|x|2
The two functions are equal if the domain of the two functions are equal, so domain f = domain g, so
g(x)=|x|2 g(x)=|x|.|x| g(x)=|xx| =|x21 = x2 =f(x)
Therefore f(x) and g(x) OR the domain f and g are equal.
(b)
f :ZZ-Z,where f(x,y)=|x+y|. g:Z x Z Z,where g(x,y)=|x|+|y|.
Since there are no restrictions on the domain of the functions for f and g, then x = 1 and y = -1 is within the ZxZ, so if the coordinates (1,-1) was plugged into f(,y) and g(,y), then the functions are not equal.
f(x,y)=|x+yl f(1, -1) = |1 + (1)| = |1 - 1| = |0|
snhu
= 0
g(x,y)=|x|+|y1 g(1, -1)= |1|+|-1| =[1+[-1] =1+1 = 2
therefore f(x,y) g(x,y) at f(1,-1) and g(1,-1