how cpme (1+x)^4 is neither an odd nor an even function ????

Question

noelgreco · Answer

Because $$f(-x)\neq f(x)  and   f(-x)\neq -f(x)$$

helder_edwin · Answer

an even function is symetric with respect to the y-axis. an odd function is symetric with respect to the origin. this function is neither.

furthermore, if $E=\{f\in\mathbb{R}^\mathbb{R}:f(x)=f(-x)\}$ and $O=\{f\in\mathbb{R}^\mathbb{R}:-f(x)=f(-x)\}$ then $E\cup O\varsubsetneq\mathbb{R}^\mathbb{R}$.
this function is an example of this.

anonymous · Answer

another way of finding the answer is to expand the expression : (1+x)^4 can also be considered as the polynomial 1+4x+6x^2+4x^3+x^4. Since the polynomial is a combination of both even and odd powers of x, it cannot be even or odd.  All of the other answers are quite true, but doing some algebraic expansion can also help.