Proof: f = g + h, Even & Odd Functions

[javi438]

say function f is continuous on (-\infty,\infty). show that f can be written as f = g + h, where g is an even function and h is an odd function.

help pleaseee!

 

[d_leet]

If f(x)=g(x)+h(x) where g is even and h is odd, then what is f(-x)?

 

[mjsd]

yeah, use those properties to help you construct your g and h out of f's

 

[javi438]

f(-x) = g(-x) + h(-x)
f(-x) = g(x) - h(x)
= g(x) + (-h(x))

is that it??

 

[d_leet]

Ok, then what is f(x)+f(-x)? Then what is g(x), and finally what is h(x)?