If f: A →B is an onto function defined by f(x)=3 x-4 and A={0,1,2,3}, then the co-domain of fis

step 1 Hello students in this problem a function f from A to B is defined and this is onto function and

If f: A →B is an onto function defined by f(x)=3 x-4 and...

If $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is an onto function defined by $\mathrm{f}(\mathrm{x})=3 \mathrm{x}-4$ and $\mathrm{A}=\{0,1,2,3\}$, then the co-domain of fis
(1) $\{-4,0,2,5\}$.
(2) $\{-1,2,5,6\}$.
(3) $\{-4,-1,2,5\}$.
(4) None of these

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Key Concepts

Mapping Rule

The mapping rule of a function is a specific formula or relation that assigns each element from the domain to an element in the codomain. It defines how inputs are systematically transformed into outputs, allowing for the analysis of the function's behavior.

Onto Function (Surjection)

An onto function, or surjective function, is one in which every element of the codomain is the image of at least one element from the domain. This means that the function completely 'covers' the codomain, ensuring that there are no unused elements in the target set.

Domain

The domain of a function is the complete set of all possible input values for which the function is defined. It provides the starting points from which the function maps to the codomain.

Codomain vs Range

The codomain of a function is the set of potential outputs defined as part of the function's structure, while the range is the subset of values that are actually obtained when the function is applied to all elements of the domain. In the context of an onto function, the range and codomain are identical since every element in the codomain is realized by the function.

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