Question

What is domain of the function?

y =(pic about to be posted)

x ≤ – 1
x >1
x ≥ –1
x ≥ 1

Answer 1

\[x \ge-1\]

Answer 2

\[\LARGE \sqrt{3x+3}\]
so we can't have negative square root, that would send us to imaginary numbers, which we want to avoid. So all expression under square root should be equal or greater than 0.
we write it like:
\[\LARGE 3x+3\geq 0\]
subtract 3 to both sides
\[\LARGE 3x+3-3\geq 0-3\]
\[\LARGE 3x\geq -3\]
divide both sides by 3 and you'll have:
\[\LARGE \frac{3x}{3}\geq -\frac{3}{3} \]
\[\LARGE x\geq -1 \]


REMEMBER. when you're dealing with inequalities. EVERY TIME you multiply\divide by a negative number. You swap sign.
example:
\[\LARGE -x\geq -3\]
when we multiply this by a negative number we have to change its sign
so:
\[\LARGE x\leq 3\]

but in your case we didn't have to multiply\divide by a negative number. That's why we didn't swap anything... :)