Question

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If $\mathrm{f}(\mathrm{x})=|\mathrm{x}|+|\mathrm{x}-1|$, then which one of the following is correct?

MathematicsContinuity and DifferentiabilityNDANDA 2018 (Phase 1)

Options:

A $\mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=0$ and $\mathrm{x}=1$
B $\mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=0$ but not at $\mathrm{x}=1$
C $\mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=1$ but not at $\mathrm{x}=0$
D $\mathrm{f}(\mathrm{x})$ is neither continuous at $\mathrm{x}=0$ nor at $\mathrm{x}=1$