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

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:AB which reads ‘f’ is a function from A to B ‘f’ maps A to B.

Let f:AB,then the set A is known as the domain of f & the set B is known as co - domain of f .The set of images of all the elements of A is known as the range of f.

Thus, Domain of f = {a|a A,(a,f(a)) f )

Range of f = {f(a) | a A ,f(a) B }

Example: The domain of y = sin x is all values of x i.e. 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 ≤ y ≤ 1.

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