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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Functions

NDA 2022 · Mathematics · Functions

What is the domain of the function f(x)= 1-(x-1)^2 ?

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

Options

  1. A(0,1)(0,1)
  2. B[−1,1][-1,1]
  3. C(0,2)(0,2)
  4. D[0,2][0,2]

Correct answer

D. [0,2][0,2]

Step-by-step solution

∵f(x)=1−(x−1)2∴1−(x−1)2≥0⇒1−x2+2x−1≥0⇒−x(x−2)≥0⇒x(x−2)≤0−+−+02∴x∈[0,2]\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}
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