If $f(x)=\left \lfloor{x}\right \rfloor$ and $g(x)=\left \lceil{x}\right \rceil$, express $g(x)$ in terms of $f(x)$ and $x$.

Question

If $f(x)=\left \lfloor{x}\right \rfloor$ and $g(x)=\left \lceil{x}\right \rceil$, express $g(x)$ in terms of $f(x)$ and $x$.

I am not too sure how to tackle this problem (I am new when it comes to these functions, so the simpler the solution the better!).

Looking at similar questions $-\left \lfloor{-x}\right \rfloor$ seems to be the answer, but the answer from the book I am using says (sorry this is an image, but I am not confident to type it out!):

Any help or explanation would be greatly appreciated.