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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

What is the range of the function f(x)=1- x defined on entire real...

What is the range of the function f(x)=1−sin⁡xf(x)=1-\sin x defined on entire real line?

Options

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

Correct answer

B. [0,2][0,2]

Step-by-step solution

f(x)=1−sin⁡x−1d′′sin⁡xd′′11ee′′−sin⁡xe"−12e"1−sin⁡xe"0∴ Range =[0,2]\begin{aligned} & f(x)=1-\sin x \\ & -1 \mathrm{ d}^{\prime \prime} \sin x \mathrm{ d}^{\prime \prime} 1 \\ & 1 \mathrm{e} \mathrm{e}^{\prime \prime}-\sin x \mathrm{e} "-1 \\ & 2 \mathrm{e} " 1-\sin x \mathrm{e} " 0 \\ & \therefore \text{ Range }=[0,2]\end{aligned}
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