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Question

If f(x)={|x|−3,x<1|x−2|+a,x≥1 and g(x)={2−|x|,x<2sgn(x)−b,x≥2 and h(x)=f(x)+g(x) is discontinuous at exactly one point, then which of the following values of a and b are possible.

A
a=3,b=0
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B
a=2,b=1
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C
a=2,b=0
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D
a=3,b=1
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