Suppose that the functions f and g are defined as follows fx

Suppose that the functions f and g are defined as follows. f(x) = x/x - 3 g(x) = x + 4/x - 3 Find f/g. Then, give its domain using an interval or union of intervals. Simplify your answers. (f/g) (x) = Domain of f/g:

Solution

f(x) = x/(x-3)

g(x) = (x+4) / (x-3)

f/g = f(x)/ g(x)

f/g = x / (x-3) / (x+4) / (x-3) = x / (x+4)

domain of f/g is all values of x except x = -4

interval notation of domain is (-infinity , -4) U (-4 , + infinity )