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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Functions

NDA 2019 · Mathematics · Functions

The domain of the function f(x)= (2-x)(x-3) is

The domain of the function f(x)=(2−x)(x−3)\mathrm{f}(\mathrm{x})=\sqrt{(2-x)(x-3)} is

Options

  1. A(0,∞)(0, \infty)
  2. B[0,∞][0, \infty]
  3. C[2,3][2,3]
  4. D(2,3)(2,3)

Correct answer

C. [2,3][2,3]

Step-by-step solution

f(x)=(2−x)(x−3)Here, (2−x)(x−3)≥0⇒−(x−2)(x−3)≥0⇒(x−2)(x−3)≤0⇒x∈[2,3]\begin{aligned} & \quad f(x)=\sqrt{(2-x)(x-3)} \\ & \text{Here, }(2-\mathrm{x})(\mathrm{x}-3) \geq 0 \\ & \Rightarrow-(\mathrm{x}-2)(\mathrm{x}-3) \geq 0 \\ & \Rightarrow(\mathrm{x}-2)(\mathrm{x}-3) \leq 0 \\ & \Rightarrow \mathrm{x} \in[2,3]\end{aligned}
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