A) \[f(x)\]is continuous at\[x=0\]
B) \[f(x)\]is continuous at\[x=2\]
C) \[f(x)\]is discontinuous at\[x=1\]
D) None of the above
Correct Answer: B
Solution :
\[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,f(x)=0\] \[f(0)=0,\,\,\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,f(x)=4\] \[\therefore \]\[f(x)\]is discontinuous at\[x=0\]. and \[\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,f(x)=1\underset{x\to {{1}^{+}}}{\mathop{\lim }}\,f(x)=1,\,\,f(1)=1\] \[\therefore \]\[f(x)\]is continuous at\[~x=1\]. Also, \[\underset{x\to {{2}^{-}}}{\mathop{\lim }}\,f(x)=4{{(2)}^{2}}-3(2)=0\] \[f(2)=10\] and \[\underset{x\to {{2}^{+}}}{\mathop{\lim }}\,f(x)=3(2)+4=10\] Hence, \[f(x)\]is continuous at\[x=2\].
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