Hey, I'm having trouble trying to figure out this general word problem.

I want to say that the domain of the composite should be contained within the intersection of the range of $\displaystyle f$ and the domain of $\displaystyle g$, but is this correct? And is this an acceptable way of showing that answer?7. Answer with brief Explanation or Counterexample. Is the domain of $\displaystyle f \circ g$ contained in the domain of $\displaystyle f$?

$\displaystyle D_{f \circ g}=E_{f} \cap D_{g}$ where $\displaystyle E_{f}=range\ of\ f$ and $\displaystyle D_{g}=domain\ of\ g$

What do you guys think?