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AP EAMCET · Maths · Functions

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

  1. A \([-2,2]\)
  2. B \([-\sqrt{14}, 0]\)
  3. C \([2, \infty]\)
  4. D \([-2,0]\)
Verified Solution

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, \(y^2=14-(x+3)^2\)…