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Could someone read over my method? My teacher didn't give us notes, so I'm making my own...

For composite functions, for a general method to find the domain and range of them:

  1. Make inner function's range a subset of outer function's domain if necessary.
  2. Once this is done, the domain of the composite function = domain of inside function.
  3. For range of composite function, find end points and turning points. Deduce range off these values.

Would this be the correct approach for these types of problems?

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    there really isn't any general trick that can make thing easier, all you need to do is: clearly domain of $fg$ is domain of $g$, and range of $fg$ is just $f(g(\text{dom} g))$. It's also important to note that sometimes $fg$ isn't well defined even when $f$ and $g$ themselves are well defined: e.g. $f(x)=\sqrt{x}$ and $g(x)=-1$ so necessity is that $\text{Range}(g)\cap \text{dom}(f)\neq \emptyset$ – 2017-02-21

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