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

To check whether a function is even or odd, we need to check whether $f(-x) = f(x)$ (even) or $f(-x) = -f(x)$ (odd). 
For this function, we have: 
$f(-s) = 8(-s)^{7/6} = -8s^{7/6}$
$f(s) = 8s^{7/6}$
Therefore, $f(-s) = -f(s)$, which is the definition of an odd function. However, if we look at the domain of the function, $s$ must be positive because the power $7/6$ is not defined for negative numbers. Therefore, the function is only odd on its domain, not on the entire real line. Therefore, the correct answer is D, neither.

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