Let f and g be defined by

Question

f(x) = 9-x such that 4<x<8
g(x) = x+2 such that 1<x<5
[the "<" signs are less than or equal to]

Find the domains of both f o g and g o f algebraically. Find the range of f o g algebraically.

I got the equation for f(g(x)), which is 7-x. But how do i find the domains and range for these two composite functions?

Thanks!