Determine whether the function is odd, even, or neither.
-f(t) = t + cos t
A) Even
B) Neither
C) Odd

Question

Quizplus · Accepted Answer

A function is odd if $f(-t) = -f(t)$ for all $t$ in the domain, and even if $f(-t) = f(t)$. For $f(t) = t + \cos(t)$, $f(-t) = -t + \cos(-t)$. Since $\cos(-t) = \cos(t)$, $f(-t) = -t + \cos(t)$, which is not equal to $f(t)$ (not even) and not equal to $-f(t)$ (not odd), so the function is neither odd nor even.

Determine Whether the Function Is Odd, Even, or Neither