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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.!
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
AskiitiansExpert-IITD
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