A function f is constant from set A={1,2,3} onto set B={a, b, c} such that f(1)=a, then the rang

step 1 Hello students in this question a function f is constant from set a onto the set b set a contain

A function f is constant from set A={1,2,3} onto set B={a,...

A function $\mathrm{f}$ is constant from set $\mathrm{A}=\{1,2,3\}$ onto set $\mathrm{B}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$ such that $\mathrm{f}(1)=\mathrm{a}$, then the range of $\mathrm{f}$ is (1) $\{\mathrm{a}, \mathrm{c}\}$ (2) $\{\mathrm{a}\}$ (3) $\{\mathrm{a}, \mathrm{b}\}$ (4) $\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$

A function $\mathrm{f}$ is constant from set $\mathrm{A}=\{1,2,3\}$ onto set $\mathrm{B}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$ such that $\mathrm{f}(1)=\mathrm{a}$, then the range of $\mathrm{f}$ is
(1) $\{\mathrm{a}, \mathrm{c}\}$
(2) $\{\mathrm{a}\}$
(3) $\{\mathrm{a}, \mathrm{b}\}$
(4) $\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$

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Key Concepts

Onto Function (Surjection)

An onto function, or surjective function, is one in which every element of the codomain is mapped by at least one element of the domain. This ensures that the function’s mapping covers the entire codomain, although in the case of a constant function, if the codomain contains more than one element, the function cannot be onto.

Range of a Function

The range of a function is the set of all outputs that the function actually takes when applied to every element in its domain. It is distinguished from the codomain, which is the set of all potential outputs, and is critical in understanding the behavior and constraints of the function.

Function

A function is a rule that assigns to each element in a specified set (called the domain) exactly one element in another set (the codomain). This concept underpins much of mathematical analysis and structure, forming the basis for exploring relationships between different sets.

Constant Function

A constant function is one in which every input from the domain is mapped to the same single output in the codomain. Regardless of variations in the input values, the result remains unchanged, leading to a range that contains only one element.

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