If a relation f: A →B is defined by f(x)=x+2, where A={-1,0,1} and B={1,2,3}, then f is (1) only

step 1 Hello friends in this problem FX function is given as x plus 2 the set a the set a is minus one

If a relation f: A →B is defined by f(x)=x+2, where...

If a relation $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is defined by $\mathrm{f}(\mathrm{x})=\mathrm{x}+2$, where $\mathrm{A}=\{-1,0,1\}$ and $\mathrm{B}=\{1,2,3\}$,
then $\mathrm{f}$ is
(1) only one-one function.
(2) only onto function.
(3) bijective.
(4) None of these

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Key Concepts

Function

A function is a relation that assigns exactly one element from a set called the codomain to each element from another set called the domain. This foundational concept in mathematics ensures that every input has a unique output, which is critical in understanding mapping between sets.

One-to-One (Injective) Function

An injective function is one in which distinct elements of the domain map to distinct elements of the codomain. In other words, no two different inputs produce the same output, ensuring that the function preserves uniqueness across the mapping.

Onto (Surjective) Function

A surjective function is one where every element of the codomain is the image of at least one element from the domain. This means the mapping covers the entire codomain, making sure that there are no elements left unmatched.

Bijective Function

A bijective function is a function that is both one-to-one (injective) and onto (surjective). This implies a perfect pairing between the domain and the codomain, where every element of the domain corresponds to a unique element in the codomain, and every element of the codomain is covered.

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