Use Coupon: CART40 and get 40% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

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 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.