The function $$f(x) = \left\{ {\matrix{ {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} \cr {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| > 1} \cr } } \right.$$ is :

Question

The function
$$f(x) = \left\{ {\matrix{ {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} \cr {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| > 1} \cr } } \right.$$ is :

continuous on R–{–1} and differentiable on R–{–1, 1}

both continuous and differentiable on R–{1}

both continuous and differentiable on R–{–1}

continuous on R–{1} and differentiable on R–{–1, 1}

Solution

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