the domain is the set of all x-values for which the function is defined. basically, you need to find out what x-values "work" in these formulas.

example, for and

the domain of is , that is, all real numbers. since you can plug in any real number into and it will work, since it is a polynomial

for , the domain of is , that is, all real numbers except -2. why not -2? our function does not "work" there, because if x = -2, then we have a fraction in which the denominator is zero. dividing by zero is a no-no (see the pic)

now, find fg and f/g (do you know how?) and do the same analysis to come up with their domains. note, anything that is not in the domain of f and/or g, will not be in the domain of fg nor f/g

(i wrote the domains using interval notation. there are several ways you can write them...)