Continuous proofs

1. Oct 31, 2007

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.

2. Oct 31, 2007

d_leet

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

3. Oct 31, 2007

mjsd

4. Oct 31, 2007

javi438

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

is that it??

5. Oct 31, 2007

d_leet

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