Question 1162395
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<pre>

f(x) = {{{(f(x) + f(-x))/2}}} + {{{(f(x) - f(-x))/2}}}.



It is the decomposition of the function f(x) into the sum of two functions



    e(x) = {{{(f(x) + f(-x))/2}}}  and  o(x) = {{{(f(x) - f(-x))/2}}}.



The function e(x) is an even function;  the function o(x) is the odd function.



So, the formula (*)  gives you the required presentation.
</pre>


It is a standard statement from the <U>Elementary function theory</U> for beginner university Math students.