Q: Can the domain and range be represented by one number?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

Yes. The range can have fewer number of entries.As an extreme case, consider f(x) = 3, where x is a Real number.The domain is all Real numbers - infinitely many of them, while the range is one value: 3.A function can contain one-to-one or many-to-one relationships but one-to-many relationships are not permitted. As a result, the cardinality of the range cannot be bigger than the cardinality of the domain.

You need to know the domain in order to find the range.

A relation is a mapping between two sets, a domain and a range. A function is a relationship which allocates, to each element of the domain, exactly one element of the range although several elements of the domain may be mapped to the same element in the range.

It is the function for which all the elements of the range of the function corresponds to exactly one element of the domain.

All functions are relations with the condition that each element of the domain is paired with only one element of the range. A relation is any pairing of numbers from the domain to the range.

Related questions

Yes. The range can have fewer number of entries.As an extreme case, consider f(x) = 3, where x is a Real number.The domain is all Real numbers - infinitely many of them, while the range is one value: 3.A function can contain one-to-one or many-to-one relationships but one-to-many relationships are not permitted. As a result, the cardinality of the range cannot be bigger than the cardinality of the domain.

The domain and the range depends on the context. For example, the domain and the range can be the whole of the complex field. Or I could define the domain as {-2, 1, 5} and then the range would be {0, 3, -21}. When either one of the range and domain is defined, the other is implied.

Is it true that in a relation for each element of the domain there is only one corresponding element in the range

The domain of a function, is the range of input values which will give you a real answer.For example the domain of x+1 would be all real numbers as any number plus 1 will be another real numberThe domain of x0.5 would be all positive numbers as the answer to square root of a negative number is not realNote:x0.5 means the square root of x* * * * *Not quite. A function is a one-to-one or many-to-one mapping from a set S to a set T (which need not be a different set). A function can be one whose domain is all the cars parked in a street and the range is the second character of their registration number.A mathematical function can have the complex field as its domain and range, so a real answer is not a necessary requirement for a function.

Is it true that in a relation for each element of the domain there is only one corresponding element in the range

Yes, the domain must correspond to only one member of the range in order to be a function in a member of the domain goes to more than one member of the range it then is a relation and not a function A function is a relation but a relation isnt always a function

A function is a mapping from one set to another. It may be many-to-one or one-to-one. The first of these sets is the domain and the second set is the range. Thus, for each value x in the domain, the function allocates the value f(x) which is a value in the range. For example, if the function is f(x) = x^2 and the domain is the integers in the interval [-2, 2], then the range is the set [0, 1, 4].

A relation where each element of the domain is paired with only one element of the range is a one to one function. A one to one function may also be an onto function if all elements of the range are paired.

It is a bijection [one-to-one and onto].

You need to know the domain in order to find the range.

No it is not. The number 3, in the domain, gets mapped to more than one number in the range.

A relation is a mapping from elements of one set, called the domain, to elements of another set, called the range. The function of the three terms: relation, domain and range, is to define the parameters of a mapping which may or may not be a function.