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Question

# Let f(x) be defined in [–2,2] by f(x)={max{√4−x2,√1+x2}−2≤x≤0min{√4−x2,√1+x2}0<x≤2 . Then f(x) is

A

Continuous & differentiable at all points

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B

Discontinuous at one point & non-differentiable at more than one point

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C

Non-differentiable at more than one point & continuous at all points

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D

Discontinuous & non-differentiable at only one point

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Solution

## The correct option is B Discontinuous at one point & non-differentiable at more than one point y=√4−x2 ⇒y2=4−x2 ⇒x2+y2=4 ... (1) It is a circle with centre at (0,0) and radius equal to 2 and y=√1+x2 ⇒y2=1+x2 ⇒y2−x2=1 ... (2) which is a hyperbola Then f(x) is

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