Question

-Where does the graph of f(x) = -3√-2x - 3 start?OA. (-2,3)OB. (-3)OC. (-1,0)OD. (1,3)Reset Selection

Answer 1

In general, the domain of the square root function is

$domain(\sqrt{y})=\lbrack0,\infty)$

Therefore, for f(x) to be well defined, we need the radicand to be more or equal to 0; this is

$\begin{gathered} -2x-3\ge0 \\ \Rightarrow-2x\ge3 \\ \Rightarrow x\leq\frac{3}{-2} \end{gathered}$

Thus, finding the corresponding value of f(x) for x=-3/2

$\begin{gathered} \\ \Rightarrow f(-\frac{3}{2})=-3\sqrt{-2(-\frac{3}{2})-3}=-3\sqrt{3-3}=0 \\ \Rightarrow(-\frac{3}{2},0) \end{gathered}$

Hence, the answer is option C. (-3/2,0)