Z x Z functions and range
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Consider the set of integers Z. The set Z x Z consists of all ordered pairs of integers. In symbols,
Z x Z={(x,y):x,y∈Z}
For example, (2,-5) , (0,0) , (-127,10) , and (-5,2) are all distinct elements of Z x Z.
Notice that the order matters; (2,-5) and (-5,2) are different elements of Z x Z.
Now let?s define a few functions on Z x Z:
f(x,y)=x*y
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h(x,y)=x^y
(a) What is the range of each of these functions? In other words, is the image an integer, a rational number or only a real number?
(b) For which of these functions (if any) is the image of (x,y) equal to the image of (y,x)?
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The solution examines Z x Z functions and range.
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See the attached file.
6. Consider the set of integers. The set x consists of all ordered pairs of integers. In symbols,
x
For example, (2,-5) , (0,0) , (-127,10) , and (-5,2) are all distinct elements of x .
Notice that the order matters; (2,-5) and (-5,2) are different elements of x .
Now let's define a few functions on x :
(a) What is the range of ...
Purchase this Solution
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