GATE 2013 CS (CS1) – Question 32
Which function is continuous at x=3?
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Correct answer: (A) f(3)=2; f(x)=x−1 for x>3; f(x)=(x+3)/3 for x<3
Explanation
In A, the left limit is (3+3)/3=2 and the right limit is 3−1=2, both matching f(3)=2. B has limit five but value four. C has left/value six and right limit minus one. D is undefined and singular at three. Thus only A is continuous.