I have to find the domain for $f(x) = \frac{\ln x}{x}$
Naturally, $x$ must be larger than $0$ and $x$ can't be $0$ so $x > 0$.
But when I graphed the function, it has two "parts", one in the positive quadrant and another where $x$ is negative. So I'm not sure how the negative part exists, if you can't put any negative numbers into log?
Also, they ask me to find where $\frac{\ln x}{x}$ cuts through $x$, so I put $\frac{\ln x}{x} = 0$ so $x =1$. But if the negative part exists, the functions also cuts the graph at $x=-1$. But we are not allowed to input $-1$ into $\log(x)$!
So, how is it possible?