SOLUTION: Suppose that f(x) is defined ∀x ∈ (−∞,∞). Show that f(x) = e(x) + o(x), where e is an even function and o is an odd function.

Question 1162395: Suppose that f(x) is defined ∀x ∈ (−∞,∞). Show that f(x) = e(x) + o(x), where e is an even function and o is an odd function.

Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.


f(x) =  + .



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



    e(x) =   and  o(x) = .



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



So, the formula (*)  gives you the required presentation.

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

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