The range of the function $f(x)=-\sqrt{-x^2-6 x-5}$ is

• A

  $[0,2]$
• Correct answer
  B

  $[-2,0]$
• C

  $[-2,2]$
• D

  $(-\infty, 2]$

Solution

$\begin{aligned} & -x^2-6 x-5 \\ D= & 36-4(-1)(-5)=16\end{aligned}$
$\begin{array}{ll}\therefore \quad & -x^2-6 x-5 \in(-\infty, 4] \\ \text { for } & \sqrt{-x^2-6 x-5} \\ & f(x) \in[0,2] \\ & -f(x) \in[-2,0]\end{array}$

Hence, the correct answer is option: 'B'.