0 votes 0 votes Which of the following is a mapping or total function 1) f is defined on RXR f(x)=1 ;x=5t, t ℇ Z =0 ;x=5t+1, t ℇ Z 2)1) f is defined on RXZ f(x)=1 ;x=5t, t ℇ Z =0 ;x=5t+1, t ℇ Z Vasu_gate2017 asked Oct 21, 2016 Vasu_gate2017 227 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 1 votes 1 votes We say a function f : A --> B i.e. function from A to B is a total function or mapping if the domain of the function f is equal to the cardinality of set A. In the first example we are given f(x) so x should be considered for domain. Given x = 5t where t is given that it belongs to integers (Z).So x also belongs to integers only and not real numbers But f is defined from R × R, so cardinality of A set in given A --> B is the set of real numbers. Hence the domain does not cover all elements of A set. Since only specific integers are covered only. Hence the given function is a partial function not a total function. Similarly the 2nd set is also defined on R × Z but the domain is the set of integers only. Hence it is not total function as well. Had the function been defined Z × R or Z × Z then the function would be total function. Habibkhan answered Oct 21, 2016 selected Oct 23, 2016 by Vasu_gate2017 Habibkhan comment Share Follow See all 0 reply Please log in or register to add a comment.