CBSE BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
Question
Define a function as a set of ordered pairs.
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Answer
Function: Let $A$ and $B$ be two non$-$empty sets. A relation $A$ to $B$
i.e., a sub$-$set of $A \times B,$ is called a function $($or a mapping a map$)$ from $A$ to $B,$ if
For each $\text{a}\in\text{A}$ there exists $\text{b}\in\text{B}$ such that $(\text{a},\text{b})\in\text{f}$
$(\text{a},\text{b})\in\text{f}$ and $(\text{a},\text{c})\in\text{f}$
$\Rightarrow\text{ b} =\text{c}$
If $(\text{a},\text{b})\in\text{f},$ then $'b\ '$ is called the image of $'a\ '$ under $f.$
If a function is expresed as the set of ordered pairs, the domain $f$ is the set of all first components of members of $f$ and the range of $f$ is the set of second components of members of $f.$
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