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Continuity of a Function

Let fx= cos...

Question

Let $f (x) = {cos}^{- 1} (cos x)$ , then $f (x)$ is

continuous at

x = π

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discontinuous at

x = - π

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differentiable at

x = 0

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non-differentiable at

x = π

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Solution

The correct options are
A continuous at $x = π$
D non-differentiable at $x = π$
The range of $c o s^{- 1} x$ is $[0, π]$ . Hence, the graph of $f (x) = {cos}^{- 1} (cos x)$ is as shown in the figure.
From the graph, we can conclude that $f (x)$ is continuous at $x = π$ , but not differentiable.
It is not differentiable at $x = 0$ and is continuous at $x = - π$ .
Hence, options A and D are correct.

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