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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Functions

NDA 2023 · Mathematics · Functions

Let f(x)= 2-x + 2+x . What is the domain of the function?

Let f(x)=2−x+2+xf(x)=\sqrt{2-x}+\sqrt{2+x}. What is the domain of the function?

Options

  1. A(−2,2)(-2,2)
  2. B[−2,2][-2,2]
  3. CR−(−2,2)\mathrm{R}-(-2,2)
  4. DR−[−2,2]\mathrm{R}-[-2,2]

Correct answer

B. [−2,2][-2,2]

Step-by-step solution

Given, f(x)=2−x+2+x\mathrm{f}(\mathrm{x})=\sqrt{2-\mathrm{x}}+\sqrt{2+\mathrm{x}} for Domain, 2−x≥0 and 2−x≥0⇒2≥x and x≥−2⇒−2≤x≤2⇒x∈[−2,2]\begin{aligned} & 2-x \geq 0 \text{ and } 2-x \geq 0 \\ & \Rightarrow 2 \geq x \text{ and } x \geq-2 \Rightarrow-2 \leq x \leq 2 \\ & \Rightarrow x \in[-2,2] \end{aligned}
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