Could someone please help me answer this question?

Question

Let f={(-3,0),(-1,8),(2,3)} and g={(-3,0),(1,1),(2,6)(4,-1)}. Find g/f and state its domain and the its function.

Answer 1

g/f is the function that sends x to g(x)/f(x). For x to be in the domain of g/f, both g(x) and f(x) need to be defined. We see that f(x) is defined for x = -3, -1, 2 and g(x) is defined for x = -3, 1, 2, 4. Therefore both f(x) and g(x) are defined for x = -3, 2.

(g/f)(-3) = g(-3) / f(-3) = 0/0 is not defined (can't divide by zero), so -3 is not in the domain of g/f

(g/f)(2) = g(2)/f(2) = 6/3 = 2.

Therefore the domain of g/f is {2} and the function (as a set of ordered pairs) is {(2,2)}.