I have some limits I am supposed to find and I'm having trouble understanding the question. 

Given: 

> 
> $$f(x) = \begin{cases} 2 & \text{ if } \left \lceil x \right \rceil
> \text{is even}\\-1 & \text{ if } \left \lceil x \right \rceil
> \text{is odd} \end{cases}$$
> 
> 
> $g(x) = f\left(\frac{1}{x}\right)$
> 
> 
> 

what does $g(x) = f\left(\frac{1}{x}\right)$ mean? (maybe I'm making it more complicated than it should be in my head, it's supposed to be a 'challenge' problem.) 

example: $g\left(\frac{1}{3}\right)$, does that mean $g\left(\frac{1}{\frac{1}{3}}\right)$ so then $g(3) = -1$ ?

or like a composite function where $g\left(\frac{1}{3}\right)$ is odd so $f\left(\frac{1}{3}\right) = -1$ then $g(x) = \frac{1}{-1} = -1$?

I realize both come out to $-1$, but I think it makes a difference for when I have to find the limits. Or maybe not?