prove every fcn defined at (-a,a) is sum of odd, even fcns

[transgalactic]

prove that every function which is defined at (-a,a) could be written as a sum of odd and even functions??

i know that odd function is f(-x)=-f(x) and even is f(-x)=f(x) but how to prove what they want?

 

[PAULK]

prove that every function which is defined at (-a,a) could be written as a sum of odd and even functions??

i know that odd function is f(-x)=-f(x) and even is f(-x)=f(x) but how to prove what they want?

Easy:

Write:
f(x) + f(-x)
even(x) = ------------
2

f(x) - f(-x)
odd(x) = ------------
2

Can you do the rest?