AP EAMCET · Maths · Functions
The domain of the real valued function \(f(x)=\sqrt{9-\sqrt{x^2-144}}\), is
- A \([-15,-12] \cup[12,15]\)
- B \((-\infty,-12] \cup[12, \infty]\)
- C \([-15,15]\)
- D \([-12,12]\)
Answer & Solution
Correct Answer
(A) \([-15,-12] \cup[12,15]\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & x^2-144 \geq 0 \Rightarrow|x| \geq 12 \\ & \Rightarrow 9-\sqrt{x^2-144} \geq 0 \Rightarrow 9 \geq \sqrt{x^2-144} \\ & \Rightarrow x^2 \leq 225 \Rightarrow|x| \leq 15 \Rightarrow 12 \leq|x| \leq 15 \\ & \Rightarrow x \in[-15,-12] \cup[12,15] .\end{aligned}\)
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