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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
The range of $f(x)=\cos x-\sin x$ is
  • A
    (-1, 1)
  • B
    [-1, 1)
  • C
    $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$
  • ✓
    $[-\sqrt{2}, \sqrt{2}]$
✓

Answer

Correct option: D.
$[-\sqrt{2}, \sqrt{2}]$
(D)
Since maximum and minimum values of $\cos -\sin x$ are $\sqrt{2}$ and $-\sqrt{2}$ respectively, therefore range of $f (x)$ is $[-\sqrt{2}, \sqrt{2}]$.

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