Final answer:
The domain of the given relation R={(x,y):y=“x−1”,x∈Z and “x”≤3} is {-3, -2, -1, 0, 1, 2, 3}, and its range is {0, 1, 2, 3, 4}, determined by substituting each domain value into the function and considering it represents the absolute value.
Step-by-step explanation:
Finding Domain and Range
To find the domain and range of the relation R={(x,y):y=“x−1”,x∈Z and “x”≤3}, we first consider the conditions given. The domain is the set of all possible x values, and here it is specified that x belongs to the set of integers (Z) and must satisfy the inequality “x”≤3. Considering these conditions, the domain is therefore {-3, -2, -1, 0, 1, 2, 3}.
Now, to find the range, we look at the function y=“x−1” and substitute each value from the domain into this function. Since y is the absolute value of x-1, the range will only include non-negative values. By substituting each element from the domain, we find the corresponding y values and deduce that the range of R is {0, 1, 2, 3, 4}.