Since every function can be divided in a even and a odd part: f_e(x)=(f(x)+f(−x))/(2) f_o(x)=(f(x)−f(−x))/(2) f(x)=f_e(x)+f_o(x). How can I obtain the function by it's even part?

cousinhaui

cousinhaui

Answered question

2022-10-24

Since every function can be divided in a even and a odd part:
f e ( x ) = f ( x ) + f ( x ) 2
f o ( x ) = f ( x ) f ( x ) 2
f ( x ) = f e ( x ) + f o ( x )
How can I obtain the function by it's even part?

Answer & Explanation

latatuy

latatuy

Beginner2022-10-25Added 12 answers

You can't. Just consider for example even functions : they have the function 0 as odd part so you can't recover the function from the function 0.
Krish Logan

Krish Logan

Beginner2022-10-26Added 4 answers

You can't obtain f from just fe or just fo. Information gets lost. For example take a function f and then define g ( x ) = f ( x ) + sin ( x ) and h ( x ) = f ( x ) + cos ( x ), then we have g e ( x ) = f e ( x ) and g o ( x ) = f o ( x ) + sin ( x ) as well as h e ( x ) = f e ( x ) + cos ( x ) and h o ( x ) = f o ( x ). As you can see the even parts can be identical while the odd parts aren't and vice versa

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