Consider these functions.
This is my crazy calculus professor coming up with this stuff.
He wants us to show that if f is any function, then it can be written as the sum of even and odd functions. That is, if f[even] is an even function and
f[odd] is an odd function, then:
f(x) = f[even](x) + f[odd](x)
He gives an example.
Example:
For f(x) = 1/(1+x), we can take f[even](x)=1/(1-x^2) and f[odd](x)=-x/(1-x^2).
You can check for yourself that f[even](x) is in fact even and that f[odd](x) is indeed odd. And also you can see that:
f[even]+f[odd]=[1/(1-x^2)] +[-x/(1-x^2)]=(1-x)/(1-x^2)=1/(1+x)=f(x)
Even with this example, I am still confused as to how to show....(see paragraph one)