What are even and odd functions?

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Answer 1 · 2014-11-12T20:25:13

Even & Odd Functions

A function $f (x)$ $f(x)$ is said to be ${("even if "f(-x)=f(x)),("odd if "f(-x)=-f(x)):}$

Note that the graph of an even function is symmetric about the $y$ -axis, and the graph of an odd function is symmetric about the origin.

Examples

$f(x)=x^4+3x^2+5$ is an even function since

$f(-x)=(-x)^4+(-x)^2+5=x^4+3x^2+5=f(x)$

$g(x)=x^5-x^3+2x$ is an odd function since

$g(-x)=(-x)^5-(-x)^3+2(-x)=-x^5+x^3-2x=-f(x)$

I hope that this was helpful.