Define a function. What do you mean by the domain and range of a funct

1.	Define a function. What do you mean by the domain and range of a function? Give examples.
Answer» 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→B which reads ‘f’ is a function from A to B ‘f’ maps A to B Let f:A→B,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 between −1 and 1. We could write this as −1 ≤ y ≤ 1.

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

Answer»

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→B which reads ‘f’ is a function from A to B ‘f’ maps A to B

Let f:A→B,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 between −1 and 1. We could write this as −1 ≤ y ≤ 1.

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