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AP EAMCET · Maths · Functions

The domain of the real valued function \(f(x)=\frac{\sqrt{2-x}+\sqrt{1+x}}{\sqrt{x+3}}\) is

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

Answer & Solution

Correct Answer

(A) \([-1,2]\)

Step-by-step Solution

Detailed explanation

Given, function is \[ \begin{aligned} & f(x)=\frac{\sqrt{2-x}+\sqrt{1+x}}{\sqrt{x+3}} \\ & x+3>0 \Rightarrow x>-3 ...(i)\\ & 2-x \geq 0 \Rightarrow x \leq 2 ...(ii)\\ & 1+x \geq 0 \Rightarrow x \geq-1...(iii) \end{aligned} \] From the above three inequalities, it can be…