Find the domain of the composite function f◦g.

Question

Find the domain of the composite function f◦g.
F(x)= 3/(x-3); g(x)= 2/x

Answer 1

f◦g = f(g) = 3/(g-3)
= 3/((2/x)-3)
= 3/((2-3x)/x)
= (3x)/(2-3x)

It looks like the domain of f◦g is all reals except x=2/3, but we also have to exclude x=0, since g is not defined there.