Question

How do you determine if `f(t)= ( t^4 tan t ) / (2 + cos t)` is an even or odd function?

Answer 1

Find `f(-t) = -f(t)` for any `t`, so `f(t)` is an odd function.

Explanation:

An even function satisfies `f(-x) = f(x)` for all `x` in its domain.

An odd function satisfies `f(-x) = -f(x)` for all `x` in its domain.

In our example:

`f(-t) = ((-t)^4 tan (-t))/(2 + cos (-t))`

`=(t^4 *(-tan(t)))/(2+cos(t))`

`=-(t^4 tan t)/(2 + cos t)`

`=-f(t)`

So `f(t)` is an odd function.