what is the largest domain of the following functions
f(x)=3x5 f(x)=square root of (x+4)
f(x)= 2 over x4 f(x)= sqaure root
of (x29)
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) = 3x5
(2)f(x) =sqrt(x+4)
(3)f(x)= 2/(x4)
(3)f(x)= sqrt(x^29)
(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 nonnegative). Thus x => 4 is the domain; the range is 0 and the positive reals.
The 3rd problem requires you to see where x^29=>0. This is the same as x=>3 or x=<3 or x=>3. The range is again nonneg. 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.
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