### Instruction: Is
\[f(x) = \frac{5^x - 1}{5^x + 1}\]an even function, odd function, or neither?

Enter "odd", "even", or "neither".### Response: Let's find $f(-x)$.
If we plug in $-x$ for $x$, we get $\frac{5^{-x} - 1}{5^{-x} + 1}$.
Let's simplify that by multiplying the top and bottom by $5^x$.
So we get $\frac{1 - 5^x}{1 + 5^x}$.
That's not the same as $f(x)$, so it's not an even function.
But it is equal to $-f(x)$, so it is an odd function.