Basics of Function

A relation f from a set A to set B is said to be a function if every element of set A has one and only one image in set B.
Vertical line test is used to determine if a relation is a function or not. A relation is a function if vertical lines intersect the graph only at one point.
Let A and B be two non empty sets. Then, a function ‘f ’ from set A to set B is a rule or method that associates the elements of set A to the elements of set B such that:
(i) All the elements of set A are associated with the elements of set B.
(ii) An element of set A is associated with a unique element in set B.
Let A and B be two non empty sets. Then, a relation f from A to B, i.e., a subset of A x B, with domain A is called a function, if
(i) No two different ordered pairs in f have the same first element.
(ii) Each element of A appears in some ordered pairs of f.
Let f : A ? B, be a function from set A to set B, then
1)  The set A is known as domain of f.
2) The set B is known as the co-domain of f.
3) The set of all the f-images of the elements of A is known as the range of f.
A function which has either R (the set of real numbers) or one of its subsets as its range is called a real valued function.
A function which has either R (the set of real numbers) or one of its subsets as both its domain and range is called a real function.
The domain of the real function f(x) is the set of all those real numbers for which, the expression for f(x) or the formula for f(x) assumes real values only. In other words, it is the set of all those real numbers for which, f(x) is meaningful.
The range of a real function of a real variable is the set of all real values taken by f(x) at the points in its domain.

Keywords: Identity Function, Constant Function, Polynomial Function, Rational Function, Modulus Function, Signum Function, Greatest Integer Function

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  • Q1

    If A x B = {(a, 1), (b, 3), (a, 3), (b, 1), (a, 2), (b, 2)}, then the value of A and B are respectively equal to

    Marks:1
    Answer:

    {a, b}, {1, 2, 3}.

    Explanation:

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  • Q2

    Marks:1
    Answer:

    {(1, 3), (2, 3), (3, 3)}.

    Explanation:
     
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  • Q3

    Marks:1
    Answer:

    Explanation:

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  • Q4

    If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is

    Marks:1
    Answer:

    29

    Explanation:

    A = {2, 4, 6 }, B = { 2, 3, 5}

    No, of elements in the cartesian product A χ B = 3 × 3 = 9

    So, the number of relations from set A to B is 29

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  • Q5

    If the set A has 3 elements and the set b = {3,4,5} then find the number of elements in (A × B).

    Marks:1
    Answer:

    9

    Explanation:
    Set A has 3 elements and set B also has 3 elements. Then, number of elements in A × B = 3 × 3 = 9
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