Question 144971
The domain of F is all reals because there are no real values of x that would make F undefined.  G, on the other hand, requires that {{{y>=0}}}.  Saying G(F(x)) is the same as saying {{{y=F(x)=3-x}}}, so the question becomes 'What values of x make y less than 0?'


{{{3-x<0}}}
{{{-x<-3}}}
{{{x>3}}}


So anytime {{{x>3}}}, {{{y<0}}} and G would be undefined.  Therefore the domain of G(F(x)) is {{{x<=3}}}.  In interval notation: <big><b> ({{{infinity}}},{{{3}}}] </big></b>