Show that any function can be expressed as the sum of an odd function and even function

Prove that every function can be expressed as the sum of an -even and an odd function.

The product of an odd function and an even function is:

Statement-1: Every function can be uniquely expressed as the sum of an even function and an odd function. Statement-2: The set of values of parameter a for which the functions f(x) defined as f(x)=tan(sinx)+[(x^(2))/(a)] on the set [-3,3] is an odd function is , [9,oo)

Statement-1: Every function can be uniquely expressed as the sum of an even function and an odd function. Statement-2: The set of values of parameter a for which the functions f(x) defined as f(x)=tan(sinx)+[(x^(2))/(a)] on the set [-3,3] is an odd function is , (9,oo)

Prove that the derivative of an odd function is an even function.

Prove that the derivative of and odd function is an even function.

Prove that the derivative of an even function is an odd function and that of an odd function is an even function.

Prove that the derivative of an even function is an odd function and that of an odd function is an even function.