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Differentiability — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiability1 Mark
MCQ
The function $\text{f(x)}=\sin^{-1}(\cos\text{x})$ is:
  • A
    Discontinuous at $x = 0$
  • ✓
    Continuous at $x = 0$
  • C
    Differentiable at $x = 0$
  • D
    None of these.
✓

Answer

Correct option: B.
Continuous at $x = 0$
$\text{f(x)}=\sin^{-1}(\cos\text{x})$
$\text{f(x)}=\sin^{-1}\Big[\sin\Big(\frac{\pi}{2}-\text{x}\Big)\Big]$
$\text{f(x)}=\frac{\pi}{2}-\text{x}$
Function is continuous at $x = 0.$

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