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Class 11 Maths Notes Chapter 2
Relations and Functions
By shahigem,

Ordered Pair
An ordered pair consists of two objects or
elements in a given fixed order
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Cartesian Product of Two Sets
For any two non-empty sets A and B, the set of all
ordered pairs (a, b) where ∈ A and b ∈ B is called

the cartesian product of sets A and B and is
denoted by A × B
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A × B ≠ B × A
          2
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If atheist one of A and B is infinite, then
(A × B) is infinite and (B × A) is infinite
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The subset is derived by
describing a relationship between the first

element and the second element of the ordered
pairs in A × B
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Note:
          1
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           2
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Let R be a
relation from a set A to a set B
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Functions
A relation f from a set A to set B is said to be a
function, if every element of set A has only an
image in set B
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Real-Valued Function
A function f: A → B is called a real-valued

function if B is a subset of R (set of all real
numbers)
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Some Specific Types of Functions
Identity function: The function f: R → R defined
by f(x) = x for each x ∈ R is called identity
function
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The domain of f = R; Range off = C

Rational function: These are the real function of
type f(x)/g(x), where f(x)and g(x)are polynomial
functions of x defined in a domain, where g(x) ≠
0
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Domaim of f = R
Range of f = R+ U {0} i
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[0, ∞)

Signum function: The real function f : R → R
defined
by f(x) = (|x|/x), x ≠ 0 and 0, if x = 0
or

is called the signum function
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Domain of f = R; Range of f = Integer
Fractional part function: The real function f : R →
R defined by f(x) = {x}, x ∈ R is called the
fractional part function
f(x) = {x} = x – [x] for all x ∈R
Domain of f = R; Range of f = [0, 1)

Algebra of Real Functions
Addition of two real functions: Let f : X → R and
g : X → R be any two real functions, where X ∈ R
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Subtraction of a real function from another: Let
f : X → R and g : X → R be any two real functions,
where X ⊆ R
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Multiplication by a scalar: Let f : X → R be a real
function and K be any scalar belonging to R
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Multiplication of two real functions: Let f : X → R
and g : X → R be any two real functions, where X
⊆ R
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e
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g : X → R is defined by (fg) x = f(x)
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Quotient of two real functions: Let f and g be two
real functions defined from X → R

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