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It is an invertible function.

Q: What is the relation in which each element in the domain is mapped to exactly one element the range?

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Any function is a mapping from a domain to a codomain or range. Each element of the domain is mapped on to a unique element in the range by the function.

A relation is a mapping from one set to another. It is a function if elements of the first set are mapped to only one element from the second set. So, for example, square root is not a function because 9 can be mapped to -3 and 3.

The domain is the set {-3, -2, 0, 3}. Note that because -2 is mapped to -5 as well as 6, this relationship is not a function.

Yes, but is is not a function because 2 gets mapped to two different values (as does -3).

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It is an injective relation.

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.

For every element on the domain, the relationship must allocate a unique element in the codomain (range). Many elements in the domain can be mapped to the same element in the codomain but not the other way around. Such a relationship is a function.

The constant function is an example where each domain element is mapped to the same range element. This function always outputs the same value regardless of the input.

Each element in the domain must be mapped to one and only one element in the range. If that condition is satisfied then the mapping (or relationship) is a function. Different elements in the domain can be mapped to the same element in the range. Some elements in the range may not have any elements from the domain mapped to them. These do not matter for the mapping to be a function. They do matter in terms of the function having an inverse, but that is an entirely different matter. As an illustration, consider the mapping from the domain [-10, 10] to the range [-10, 100] with the mapping defined by y = x2.

Any function is a mapping from a domain to a codomain or range. Each element of the domain is mapped on to a unique element in the range by the function.

It can be mapped to only one value.

Humans need relationships with other people to be happy for the most part.

A relationship is a function if every element in the domain is mapped onto only one element in the codomain (range). In graph terms, it means that any line parallel to the vertical axis can meet the graph in at most one point.

If there is an element of the domain that is mapped on to 0 then yes, else no.

A relation is a mapping from one set to another. It is a function if elements of the first set are mapped to only one element from the second set. So, for example, square root is not a function because 9 can be mapped to -3 and 3.

If every element of the first set is paired with exactly one element of the second set, it is called an injective (or one-to-one) function.An example of such a relation is below.Let f(x) and x be the set R (the set of all real numbers)f(x)= x3, clearly this maps every element of the first set, x, to one and only one element of the second set, f(x), even though every element of the second set is not mapped to.