You can study some online lessons to learn how to get started on

**finding the domain of a function**.

Since, in your case, you are finding f(g(x)), you will need to find the restrictions on the domains of each of f and g (which you'll find by checking for division-by-zero problems), and also you'll need to figure out the x-value for g which gives an output that would be a problem for f.

(Hint: Since you can't divide by zero, and since f(0) would create a division by zero, then you'll need to find what x-value(s),

*if any*, would cause g(x) to equal zero.)

Your work looks good to me!