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Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferentiability1 Mark
Question
The function $\text{f(x)}=\sin^{-1}(\cos\text{x})$ is:
  1. Discontinuous at x = 0
  2. Continuous at x = 0
  3. Differentiable at x = 0
  4. None of these.
✓

Answer

  1. Continuous at x = 0

Solution:

$\text{f(x)}=\sin^{-1}(\cos\text{x})$

$\text{f(x)}=\sin^{-1}\Big[\sin\Big(\frac{\pi}{2}-\text{x}\Big)\Big]$

$\text{f(x)}=\frac{\pi}{2}-\text{x}$

Function is continuous at x = 0.

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