Splitting a function into odd and even parts

[Hazzattack]

Hi, I've been looking at Fourier transforms, odd and even functions and such recently. But I'm a little confused about how exactly you split a function up. I know the general formula and seen the derivation, however when i do it with a proper function i never seem to get the correct answer. Was hoping someone might be able to illustrate with the following example how they obtained the final answer, explaining while going would be a huge benefit and I'm grateful for any guidance that can be offered.

For example;

Split the function f(x) = (1 + x) e^
x
into odd and even parts. Express your result in
terms of x, cosh x and sinh x.

The general formula from the Mary boas Maths/Physics book;

f(x) = ((f(x) + f(-x))/2) + ((f(x)-f(-x))/2)

Thanks again.

 

[mathwonk]

try it on e^x, and then on xe^x. the second one should be pretty easy after doing the first one (why?).

and try e^(ix), since presumably you know that answer.

 

[Hazzattack]

Just to check. When I'm using that general formula where it says f(x) do i just plug the function? and where it is f(-x) plug but changing the x's and see what it forms.