Algebraically determine whether the function below is even, odd, or neither.
$f ( s ) = 8 s ^ { 7 / 6 }$
A) even
B) odd
C) cannot be determined
D) neither

Question

Quizplus · Accepted Answer

The function $f(s) = 8s^{7/6}$ is neither even nor odd because it does not satisfy the conditions for either. For a function to be even, $f(-s) = f(s)$ must hold, which is not the case here since $f(-s) = 8(-s)^{7/6}$ does not equal $8s^{7/6}$. For a function to be odd, $f(-s) = -f(s)$ must hold, which is also not the case here since $8(-s)^{7/6}$ does not equal $-8s^{7/6}$.

Algebraically Determine Whether the Function Below Is Even, Odd, or Neither