Q.The function $f(x) = \begin{cases} x + |x| & x < 0 \ 2x + |x| & x \ge 0 \end{cases}$ is

continuous everywhere but not differentiable at

x=0

differentiable everywhere

not continuous at

x=0

continuous only at

x=0

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.The function f(x)={x+∣x∣x<0 2x+∣x∣x≥0f(x) = \begin{cases} x + |x| & x < 0 \ 2x + |x| & x \ge 0 \end{cases}f(x)={x+∣x∣​x<0 2x+∣x∣​x≥0​ is