#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# Every real valued function can be expressed uniquely as the sum of an even and odd function.Is this true..? if yes please explain with some example.! AKASH GOYAL AskiitiansExpert-IITD
419 Points
11 years ago

Dear Mukul

take a function y=f(x)

f(x)can be written as

f(x)= [f(x)+f(-x)]/2  +   [f(x)-f(-x)]/2

= h(x)               +   g(x)

h(x)= [f(x)+f(-x)]/2

h(-x)=[f(-x)+f(x)]/2 = h(x)  ----->Even function

now g(x)=[f(x)-f(-x)]/2

g(-x)=[f(-x)-f(x)]/2  = -[f(x)-f(-x)]/2=-g(x)-------> ODD function

hence every real valued function f(x) can be expressed as a sum of function h(x) and g(x) which are even and odd respectively. you can verify it by taking f(x) some function. try it.

All the best.

AKASH GOYAL

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.