Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
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)
Whereas,
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.
Exercise
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 askIITians.com to study topics pertaining to the IIT JEE and AIEEE syllabus for free.
To read more, Buy study materials of Set Relations and Functions comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Composite Functions Problem of finding out fog and...
Bounded and Unbounded Function Let a function be...
Set Theory Table of Content Set Union of Sets...
Graphical Representation of a Function The...
Greatest Integer Function The function f(x) : R...
Graphical Representation of a Function 10....
Constant Function and the Identity Function The...
Absolute Value Function The function defined as:...
Basic Transformations on Graphs Drawing the graph...
Exponential Function Exponential and Logarithmic...
Signum Function The signum function is defined as...
Explicit and Implicit Functions If, in a function...
Periodic Function These are the function, whose...
Logarithmic Function We have observed that y = a x...
Invertible Function Let us define a function y =...
Functions Table of Content What are Functions?...
Increasing or Decreasing Function The function f...
Introduction to Functions Definition of Function:...
Inverse Function Let f : X → Y be a function...
Set, Relations and Functions – Solved...
Linear Function When the degree of P(x) and Q(x)...
Polynomial and Rational Function A function of the...
Relations Table of Content What do we mean by...
Composite Functions Another useful combination of...
Cartesian Product of Sets Table of Content Define...
Algebra of Functions Given functions f : D →...
Functions: One-One/Many-One/Into/Onto Functions...