Total Price: R

There are no items in this cart.
Continue Shopping

Even And Odd Function

A function f(x) : X → Y defined such that

        f(-x) = f(x) ∀ x ε X

is called an even function and

if f (-x) = -d(x) ∀ x ε x, then the function f(x) is called an odd function.

Graphically, an even function is symmetrical w.r.t. y-axis and odd function is symmetrical w.r.t. origin.

Note : In general all functions can be represented as sum of an even function and an odd function.

Let, a function be defined as y = f(x). It can be written as:

        => y =  (f(x) + f(-x))/2 + (f(x) - f(-x))/2

        y = F1(x) + F2(x)


        F1(-x) = (f(x) + f(-x))/2 = F1(x)

And F2(-x) = (f(-x) - f(x))/2

          = -((f(x) - f(x))/2)

          = -F2(x).

Here F1(x) is an even function and F2(x) is an odd function.


State whether the following functions are odd or even or neither.

(1)    y = x3                       

(2)    y = x4

(3)    y + x + cos x          

(4)    y = loge(x + √(x2 + 1))

AskIITians is a group of IITians which provide you free online courses and a good professional advice for IIT JEE, AIEEE and other Engineering Examination preparation. You can visit to study topics pertaining to the IIT JEE and AIEEE syllabus for free.

To know the various books of engineering ,medical and school exams, fill in the below form:

We promise that your information will be our little secret. To know more please see our Privacy Policy
We promise that your information will be our little secret. To know more please see our Privacy Policy


Signing up with Facebook allows you to connect with friends and classmates already using askIItians. It’s an easier way as well. “Relax, we won’t flood your facebook news feed!”

Ask Experts

Have any Question? Ask Experts

Post Question

Related Resources
Composite Functions Part-2

Composite Functions Problem of finding out fog and...

Bounded and Unbounded Function

Bounded and Unbounded Function Let a function be...

Set Theory

Set Theory SET A set is a well-defined collection...

Algebra of Functions

Algebra of Functions Given functions f : D →...

Graphical Representation of a Function Part-1

Graphical Representation of a Function The...

Greatest Integer Function

Greatest Integer Function The function f(x) : R...

Graphical Representation of a Function Part-2

Graphical Representation of a Function...

Polynomial And Rational Function

Polynomial And Rational Function A function of the...

Constant Function and Identity Function

Constant Function and the Identity Function The...


INEQUALITIES The following are some very useful...

Basic Transformations on Graphs

Basic Transformations on Graphs Drawing the graph...

Exponential Function

Exponential Function Exponential and Logarithmic...

Signum Function

Signum Function The signum function is defined as...

Explicit and Implicit Functions

Explicit and Implicit Functions If, in a function...

Absolute Value Function

Absolute Value Function The function defined as:...

Periodic Function

Periodic Function These are the function, whose...

Logarithmic Function

Logarithmic Function We have observed that y = a x...

Linear Function

Linear Function When the degree of P(x) and Q(x)...

Composite Functions Part-1

Composite Functions Another useful combination of...

Invertible Function Part-1

Invertible Function Let us define a function y =...

Increasing or Decreasing Function

Increasing or decreasing function The function f...

Introduction to Functions

Introduction to Functions Definition of Function:...

Functions One-One/Many-One/Into/Onto

Functions: one-one/many-one/into/onto Functions...

Inverse Function

Inverse Function Let f : X → Y be a function...

Solved Examples Part-1

Download IIT JEE Solved Examples on Set, Relations...

Cartesian Product

Cartesian Product Let A and B are two non-empty...