**Question:**

Define a function. What do you mean by the domain and range of a function? Give examples.

**Solution:**

Definition: A relation $R$ from a set $A$ to a set $B$ is called a function if each element of $A$ has a unique image in B.

It is denoted by the symbol $f: A \rightarrow B$ which reads ' $f$ ' is a function from $A$ to $B$ ' $f$ ' maps $A$ to $B$.

Let $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$, then the set $\mathrm{A}$ is known as the domain of $\mathrm{f} \&$ the set $\mathrm{B}$ is known as co - domain of $\mathrm{f}$. The set of images of all the elements of $A$ is known as the range of $f$.

Thus, Domain of $f=\{a \mid a \in A,(a, f(a)) \in f)$

Range of $f=\{f(a) \mid a \in A, f(a) \in B\}$

Example: The domain of $y=\sin x$ is all values of $x$ i.e. $\mathrm{R}$, since there are no restrictions on the values for $x$. The range of $y$ is betweeen $-1$ and 1 . We could write this as $-1 \leq y \leq 1$.