Maths · Limits, continuity and differentiability
The function =\sin ^{-1}(\cos x) \) is :
The function \( f(x)=\sin ^{-1}(\cos x) \) is :
- A. discontinuous at \( =0 \)
- B. continuous at \( =0 \)
- C. differentiable \( =0 \)
- D. none of these
Step-by-step solution
The function f(x) = sin^{-1}(cos x) is continuous at x=0 because both cos x and sin^{-1} are continuous functions, and their composition is continuous. However, it is not differentiable at x=0 because the left-hand derivative (1) and right-hand derivative (-1) differ.
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