Let $$f\left( x \right) = \left\{ {\matrix{ { - 1} & { - 2 \le x < 0} \cr {{x^2} - 1,} & {0 \le x \le 2} \cr } } \right.$$ and $g(x) = \left| {f\left( x \right)} \right| + f\left( {\left| x \right|} \right).$ Then, in the interval (–2, 2), g is :

Question

Let $$f\left( x \right) = \left\{ {\matrix{ { - 1} & { - 2 \le x < 0} \cr {{x^2} - 1,} & {0 \le x \le 2} \cr } } \right.$$ and

$g(x) = \left| {f\left( x \right)} \right| + f\left( {\left| x \right|} \right).$

Then, in the interval (–2, 2), g is :

non continuous

differentiable at all points

not differentiable at two points

not differentiable at one point

Solution

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