Show that $f \in \Theta(g)$, where $f(n) = n$ and $g(n) = n + 1/n$ I am a total beginner with the big theta notation. I need find a way to show that $f \in \Theta(g)$, where $f(n) = n$, $g(n) = n + 1/n$, and that $f, g : Z^+ \rightarrow R$. What confuses me with this problem is that I thought that "$g$" is always supposed to be "simpler" than "$f$." But I think I missed something here.

You are sort of right about thinking that "$g$" is supposed to be simpler than "$f$", but not technically right.  The formal definition says nothing about simpler.
However, in practice one is essentially always comparing something somewhat messy, on the left, with something whose behaviour is sort of clear(er) to the eye, on the right.  
For the actual verifications in this exercise, it would have made no difference if the functions had been interchanged, so probably the "colloquially standard" version should have been used.  But maybe not, once or twice.  Now you know a little more about the symmetry of the notion. 
