Question

What are even and odd functions?

Answer 1

Even & Odd Functions

A function `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.

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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)`

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I hope that this was helpful.