Question

A constant function \[\operatorname{f}:\,A\to B\] will be onto if
(a) n(A)=n(B)
(b) n(A)=1
(c) n(B)=1
(D) n(A)

Answer 1

Hint: The given function is onto function and also a constant function. When a constant function is onto, then our range is the same as co-domain and should contain only one element.

Complete step-by-step answer:
According to the question, it is given that a function, \[\operatorname{f}:\,A\to B\] is such that it is onto and a constant function.
Here, values of set A is the domain of the given function.
The domain of a function is the set from which all of the values of input of the function is taken.
Here B is the range of the given function.
Range is the image of the function. In other words, Range is the set of values that actually comes out when we put the values from the domain in the function.
As our given function is onto and it is also constant.
So our co-domain should be the same as the range and it should contain only one element.
Here B is the range of the function. So, it should be constant and should contain only one element.
According to the options given, we can see that option (C) has a constant in co-domain and also has one element.
Hence, option (C) is the correct one.

Note: In this question, one can go with option (A) because it also has one element. This is wrong. A of the function is domain not co-domain. There is a difference between domain and co-domain. Co-domain is the set of values that could possibly come out when we put the values from the domain in the given function.