Question

Help with interval notation:
My prof. Never explained interval notation, so I don't know how to write the answers to these...

a) Determine the domain of the function f(x)= {1}{\sqrt{3 x+12}}
Domain (in interval notation):
Note: Write the answer in interval notation. If the answer includes more than one interval write the intervals separated by the union symbol, U. If needed enter -\infty as - infinity and \infty as infinity .

b) Determine the domain of the function f(x) = {-4}/{x^{2}+8x} .

I know a) is all real numbers except -4, and b) should be non-zero real numbers.

Answer 1

It has been a while since I've used this notation X_X, ok so your first function is
\[f(x) = \frac{ 1 }{ \sqrt{3x+12} }\] so we have to solve what's under the square root for the domain \[3x+12>0 \implies x >- 4\] it's greater than 0 because it's under the square root and we cannot have negative in square roots. So our interval will be \[D:(-4, \infty)\] we used open brackets for -4 because we do not include it in our domain, - infinity, and infinity always have open brackets. If they were closed, it means included.

Answer 2

Thank you!

Answer 3

Can you explain the second one too? I know it has multiple intervals but I'm lost other than that.

Answer 4

\[f(x) = - \frac{ 4 }{ x^2+8x }\] is this the function?