ExamBro
ExamBro
AP EAMCET · Maths · Functions

The domain of the real valued function \(f(x)=\sqrt{9-\sqrt{x^2-144}}\), is

  1. A \([-15,-12] \cup[12,15]\)
  2. B \((-\infty,-12] \cup[12, \infty]\)
  3. C \([-15,15]\)
  4. D \([-12,12]\)
Verified Solution

Answer & Solution

Correct Answer

(A) \([-15,-12] \cup[12,15]\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & x^2-144 \geq 0 \Rightarrow|x| \geq 12 \\ & \Rightarrow 9-\sqrt{x^2-144} \geq 0 \Rightarrow 9 \geq \sqrt{x^2-144} \\ & \Rightarrow x^2 \leq 225 \Rightarrow|x| \leq 15 \Rightarrow 12 \leq|x| \leq 15 \\ & \Rightarrow x \in[-15,-12] \cup[12,15] .\end{aligned}\)