The function `f(x)=sin^(-1)(cosx)` is (a) . discontinuous at `x=0` (b). continuous at `x=0` (c) . differentiable at `x=0` (d) . non of these

Explanation

To determine the properties of the function \( f(x) = \sin^{-1}(\cos x) \) at \( x = 0 \), we will check for continuity and differentiability step by step.

### Step 1: Check Continuity at \( x = 0 \)

To check if the function is continuous at \( x = 0 \), we need to verify the following condition:
\[ \lim_{x \to 0} f(x) = f(0) \]
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