Question 110300
The domain is all values the function can take. There are two big things you can't do. You can't divide by 0 and you can't take even roots of negative numbers. 

a) {{{f(x)=sqrt(x-8)}}} So, x >=8 because if x<8 then x-8<0. So I'm not sure what notion you're using by it could be [8,inf) in interval notion or in set-builder notion {x|x=>8}

b) {{{h(x)=3x^2 + 5x - 3}}} h can take any input, so your domain is the real numbers.

c) {{{m(x)=5/(x^2+9)}}} Here, the bottom can never be 0 because {{{x^2+9>0}}}, so the domain is once again all real numbers.

d) {{{l(x)=5x-4}}} Once again, the domain is the real numbers. In b) and d) you have polynomial expressions which are always definied on the real numbers.