Question

How do you know if `S(x)=sin x/ x` is an even or odd function?

Answer 1

`S(x)` is an even function.

Explanation:

A function is EVEN if `f(-x)=f(x)`. A function is ODD if `f(-x)=-f(x)`.

Let's find `S(-x)`.

`S(-x)=stackrel"equal to -sin(x)"overbrace(sin(-x)/-x`

`S(-x)=(-sin(x))/-x`

`S(-x)=sin(x)/x=S(x)`

Thus, S(x) is an even function.