Determine the Domain and Range of the Relation
Question
Determine the domain and range of the relation
\[ S=\{(a,b):b=|a-1|,\ a\in Z,\ |a|\le3\} \]
Solution
Since \[ |a|\le3, \]
\[ a=-3,-2,-1,0,1,2,3 \]
Now,
\[ b=|a-1| \]
\[ |-3-1|=4 \]
\[ |-2-1|=3 \]
\[ |-1-1|=2 \]
\[ |0-1|=1 \]
\[ |1-1|=0 \]
\[ |2-1|=1 \]
\[ |3-1|=2 \]
Therefore,
\[ S= \{ (-3,4),(-2,3),(-1,2), \]
\[ (0,1),(1,0),(2,1),(3,2) \} \]
Domain = set of first elements
\[ \boxed{ \{-3,-2,-1,0,1,2,3\} } \]
Range = set of second elements
\[ \boxed{ \{0,1,2,3,4\} } \]