Question

If $f\left(x\right)=\{\begin{array}{cc}\frac{|x-a|}{x-a},& whenx\ne a\\ 1,& whenx=a\end{array}$ , then

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

Answer 1

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

${lim}_{x\to a-}f\left(x\right)=-1,{lim}_{x\to a+}f\left(x\right)=1,f\left(a\right)=1$