If a function maps every element in its domain to a unique element in its…
If a function maps every element in its domain to a unique element in its codomain, it is called:
Answer: A. Injective — This is the basic definition of a function. If a relation maps every element in its domain to a unique element in its codomain, it is a function. Improved…
- A.
Injective
- B.
Surjective
- C.
Bijective
- D.
Functional
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Correct answer: A
This is the basic definition of a function. If a relation maps every element in its domain to a unique element in its codomain, it is a function.
Improved explanation:
The phrase is ambiguous and can be read in two ways:
Meaning A (single-valued): each domain element is assigned exactly one element of the codomain. This is the definition of a function (single-valued relation).
Meaning B (distinct images): different elements of the domain map to different elements of the codomain. This is the definition of an injective (one-to-one) mapping.
Most likely intended answer (best choice): Injective
Injective: distinct inputs always have distinct outputs (one-to-one). If x1 ≠ x2 then f(x1) ≠ f(x2).
Surjective: every element in the codomain is the image of at least one element in the domain (onto).
Bijective: both injective and surjective (one-to-one correspondence).
Function/Functional: 'function' is the noun used for a single-valued mapping. 'Functional' is an adjective and is not the standard noun to pick as an answer here.
Therefore, if the question intended 'unique' to mean 'distinct images for distinct inputs', the correct choice is Injective. If it only meant 'each input has a single image', the proper term is 'function' (not 'functional'), which is not listed as an exact option.