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