# continuous and differentiable function

by frankpupu
Tags: continuous, differentiable, function
 P: 19 function f:R->R can be written as a sum f=f1+f2 where f1 is even and f2 is odd。then if f is continuous then f1 and f2 may be chosen continuous, and if f is differentiable then f1 and f2 can be chosen differentiable i am quiet confusing this statement , if f1 is continuous f2 is not how their sum to be continuous and differentiable as well. but i am sure this statement is true. can someone explain to me ???
 P: 380 I don't know if you could have $f_1$ continuous everywhere and $f_2$ discontinuous. A simple way that you could have two discontinuous functions sum to a continuous one is if you take cosine from $-\infty<\theta\leq 0$ and 0 when greater than zero as $f_1$ and then a similar thing but where it is defined on the positive number and 0 for the negatives (and at 0 or else it will still be discontinuous). Individually there is a discontinuity at 0, but when you add them they are continuous. This is a trivial case, but I hope it makes it clear.
Math
Emeritus