Question

If $f\left(x\right)=\{\begin{array}{cc}\frac{5}{2}-x,& whenx<2\\ 1,& whenx=2,then\\ x-\frac{3}{2},& whenx>2\end{array}$

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

Answer 1

The correct option is B f(x) is discontinuous at x = 2

${lim}_{x\to 2-}f\left(x\right)=\frac{1}{2}$ and ${lim}_{x\to 2+}f\left(x\right)=\frac{1}{2}$ and f(2) = 1