The function f(x)= ^ -1 ( ) is: 1. Discontinuous at x = 0 2. Cont… - Vidyadip

Question

The function $\text{f(x)}=\sin^{-1}(\cos\text{x})$ is:

Discontinuous at x = 0
Continuous at x = 0
Differentiable at x = 0
None of these.

✓

Answer

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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