Question

is this function even, odd, or neither? f(s)=4s^3/2

Answer 1

A function \(f(s)\) is odd if \(f(-s)=-f(s)\), or even if \(f(-s)=f(s)\), or neither if none of these are satisfied.

To test if a function is odd/even/neither, plug in \(-s\) for \(s\):
\[f(-s)=4(-s)^{3/2}\]
But, \((-s)^{3/2}=\left((-s)^3\right)^{1/2}=\left(-s^3\right)^{1/2}\). You can't take the square root of a negative number, so \(f(-s)\) is not defined for real \(s\). So, \(f(s)\) is neither even nor odd.