Given the functions, $\displaystyle f(x) = \frac{x-2}{x-5}$ and $\displaystyle g(x) = \sqrt{x + 7}$, find the following domains. Use interval notation. help (intervals)

Domain of $\displaystyle f$
Domain of $\displaystyle g$
Domain of $f + g$
Domain of $\displaystyle \frac{f}{g}$
Domain of $\displaystyle \frac{g}{f}$
Domain of $\displaystyle f(g(x))$
Domain of $\displaystyle g(f(x))$