Question

The function $f(x)=\{\begin{array}{ll}1,& \text{ if }x\ne 0\\ 2,& \text{ if }x=0\end{array}$ is not continuous at

• A. $x=0$
• B. $x=1$
• C. $x=-1$
• D. None of these

Answer 1

Answer: (A)

This function is also defined at every point. Left and the right hand limits at $x=0$ are both equal to 1 . But the value of the function at $x=0$ equals 2 which does not coincide with the common value of the left and right hand limits. Again, we note that we cannot draw the graph of the function without lifting the pen. This is yet another instance of a function being not continuous at $x=0$.