find the domain of composite function fog

Question

f(x)=x/x-4; g(x)= -1/x

please show work

Answer 1

f(g) = g/(g-4)
= (-1/x) / (-1/x - 4)
= (-1)/(-1-4x)
= 1/(4x+1)

domain is all reals except x = -1/4, 0

f(4) is not defined, but g(x) = 4 when x = -1/4.

unfortunately, g(0) is not defined, so f(g(0)) is also not defined