AP EAMCET · Maths · Functions
The range of the function \(f(x)=-\sqrt{5-6 x-x^2}\) is
- A \([-2,2]\)
- B \([-\sqrt{14}, 0]\)
- C \([2, \infty]\)
- D \([-2,0]\)
Answer & Solution
Correct Answer
(B) \([-\sqrt{14}, 0]\)
Step-by-step Solution
Detailed explanation
\(f(x)=-\sqrt{5-6 x-x^2}\) Let \(f(x)=y\) \(\begin{aligned} & \Rightarrow \quad y=-\sqrt{-\left(x^2+6 x-5\right)} \\ & \Rightarrow-y=\sqrt{-\left(x^2+6 x+9-9-5\right)} \\ & \Rightarrow-y=\sqrt{-\left\{(x+3)^2-14\right\}}\end{aligned}\) On squaring both sides, \(y^2=14-(x+3)^2\)…
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