Question

If $f\left(x\right)=\{\begin{array}{cc}1+x^2,& when0\le x\le 1\\ 1-x,& whenx>1\end{array}$, then

• A. ${lim}_{x\to 1^{+}}f\left(x\right)\ne 0$
• B. ${lim}_{x\to 1^{-}}f\left(x\right)\ne 2$
• C. f(x) is discontinuous at x = 1
• D. None of these

Answer 1

The correct option is C f(x) is discontinuous at x = 1

${lim}_{x\to 1+}f\left(x\right)=0$ and ${lim}_{x\to 1-}f\left(x\right)=1+1=2$
Hence f(x)is discontinuous at x = 1