A function {f}: {R} \\to{R} is defined as {f}({x})={x}^{2} for {x} \\geq0 and {f}({x})=-{x} for {x}

UPSC NDA Math Model Paper 1

Question : 114 of 120

Marks: +1, -0

A function f:R→R is defined as f(x)=x2 for x≥0 and f(x)=−x for x<0
Consider the following statements in respect of the above function:
1. The function is continuous at x = 0.
2. The function is differentiable at x = 0.
Which of the above statements is / are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Validate

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