Question

what is the largest domain of the following functions

f(x)=3x-5 f(x)=square root of (x+4)
f(x)= 2 over x-4 f(x)= sqaure root
of (x2-9)
f(x)= 2 over x(x+7)


Hopefully you've solved these by now. I just noticed the question and see there's no reply.
The question is
"what is the largest domain of the following functions "

(1)f(x) = 3x-5
(2)f(x) =sqrt(x+4)
(3)f(x)= 2/(x-4)
(3)f(x)= sqrt(x^2-9)
(4)f(x)= 2/(x(x+7))

For (1) I think you can see that there are no restrictions on x for the domain and the range is all reals.
For (2) you should see that the domain must be non-negative). Thus x => -4 is the domain; the range is 0 and the positive reals.
The 3rd problem requires you to see where x^2-9=>0. This is the same as |x|=>3 or x=<-3 or x=>3. The range is again non-neg. reals.
For (4) we cannot have zero in the denominator, thus the domain for x is all reals except 0 and -7. Calculating the range will probably be a challenge here. I'll let you prove that f(x) can never = 0. There is also a small interval of negative values the range doesn't take on.
...and just now I see that the question in only seeking the domain values...ok. Start a new thread if you need further assistance.