Functions

A relation R from a set A to a set B is said to be a function if for every a in A, there is a unique b in B such that (a, b) ∈R. If R is a function from A to B and (a, b) ∈ R, then b is called the image of a under the relation R and a is called the preimage of b under R. For a function R from set A to set B, set A is the domain of the function; the images of the elements in set A or the second elements in the ordered pairs form the range,while the whole of set B is the codomain of the function.

            For example, in relation since each element in A has a unique image, therefore f is a function.

Each image in B is 2 more than the square of pre-image.

Hence, the formula for f is Or

Domain = {−1, 0, 1, 2, 3}

Co-domain = {2, 3, 6, 11, 13}

Range = {2, 6, 3, 11}

Real-valued Function: A function having either R (real numbers) or one of its subsets as its range is called a real-valued function. Further, if its domain is also either R or a subset…