But take, for example:

$f(x)=\frac{3}{2x+1},x>0$

and

$g(x)=\frac{1}{x}+2,x>0$

I am so confused with the whole process of finding the ranges of functions, including those above as samples, that I can't even quite explain what or why.

Can someone please, in a very step-by-step process, detail exactly what steps you would take to get the ranges of the above functions? I tried substituting x-values (such as 0), and came up with $f(x)>3$, but that was mostly guesswork -- also, $f(x)>3$ is incorrect.

Also, is there an outline I can follow -- even for the thinking process, like check if A, check if B -- that would work every time?