For the functions f(x)=x/x+3and g(x)=7/x, find the composition (f∘g)(x) and simplify your answer as much as possible. Write the domain using interval notation

Answer 1

f(g) = g/(g+3) = (7/x) / (7/x + 3) = 7/(3x+7)
exclude from the domain values where the denominator is zero.

also,
since f(x) is undefined for x = -3, exclude values where g(x) = -3
since g(x) is undefined for x=0, exclude that as well