SOLUTION: Find domain of f(x)/g(x). f(x) = sqrt{4 - x^2} g(x) = sqrt{9 - x^2}

f(x) has the domain  4-x^2 >= 0,  where the expression under square root is non-negative.

It is the same as   x^2 <= 4,  or  |x| <= 2,  or  -2 <= x <= 2.



g(x) has the domain  9-x^2 >= 0,  where the expression under square root is non-negative.

It is the same as   x^2 <= 9,  or  |x| <= 3,  or  -3 <= x <= 3.



For function  f(x)/g(x),  the domain is the intersection (the common part)
of the two above mentioned domains.


This intersection is the smaller domain  |x| <= 2,  or  -2 <= x <= 2.    ANSWER