Question

f(x)=9/(4-radical(6x- -4). find the (implied) domain??

Answer 1

\[f(x)=\frac{9}{4-\sqrt{6x+4}}\]The denominator can't be zero, therefore:
\[4-\sqrt{6x+4}=0,\]\[4=\sqrt{6x+4},\]\[16=6x+4,\]\[12=6x,\]\[x=2.\]The domain of x is then
\[\left \{ x\in \mathbb{R}:x\neq 2 \right \}\]

Answer 2

In addition, the radicand must be nonnegative

So \[\large 6x+4\ge0\]

\[\large 6x\ge-4\]

\[\large x\ge-\frac{4}{6}\]

\[\large x\ge-\frac{2}{3}\]