Q209 / 270 · NDA 2022 (Phase 1) · Mathematics

What is the domain of the function $f(x)=\sqrt{1-(x-1)^2}$ ?

  • A
    $(0,1)$
  • B
    $[-1,1]$
  • C
    $(0,2)$
  • Correct answer
    D
    $[0,2]$

Solution

$\begin{aligned} & \because \mathrm{f}(\mathrm{x})=\sqrt{1-(\mathrm{x}-1)^2} \\ & \therefore 1-(\mathrm{x}-1)^2 \geq 0 \Rightarrow 1-\mathrm{x}^2+2 \mathrm{x}-1 \geq 0 \\ & \Rightarrow-\mathrm{x}(\mathrm{x}-2) \geq 0 \Rightarrow \mathrm{x}(\mathrm{x}-2) \leq 0 \\ & -\frac{+-+}{0 \quad 2} \\ & \therefore \mathrm{x} \in[0,2]\end{aligned}$

Hence, the correct answer is option: 'D'.

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