Which of the given functions is discontinuous?
A)$f ( x ) = \left\{ \begin{array} { c c }
\frac { 1 } { x - 11 } , & x \neq 11 \
9 , & x = 11
\end{array} \right.$

B) $f ( x ) = \left\{ \begin{array} { c c }
\frac { 1 } { x - 2 } , & x \geq 11 \
\frac { 1 } { 9 } , & x

Question

Which of the given functions is discontinuous?
A)$f ( x ) = \left\{ \begin{array} { c c } 
\frac { 1 } { x - 11 } , & x \neq 11 \
9 , & x = 11
\end{array} \right.$

B) $f ( x ) = \left\{ \begin{array} { c c } 
\frac { 1 } { x - 2 } , & x \geq 11 \
\frac { 1 } { 9 } , & x < 11
\end{array} \right.$

Quizplus · Accepted Answer

Function A is discontinuous since it has a removable discontinuity at x = 11. When x = 11, the function is defined as 9 instead of the limit which does not exist.

Function B is continuous everywhere except at x = 2 where there is a vertical asymptote, causing a non-removable infinite discontinuity.

Which of the Given Functions Is Discontinuous? A) f(x)={1x−11,x≠119,x=11f ( x ) = \left\{ \begin{array} { c c } \frac { 1 } { x - 11 } , & x \neq 11 \\9 , & x = 11\end{array} \right.f(x)={x−111​,9,​x=11x=11​

Which of the Given Functions Is Discontinuous?
A) $f ( x ) = \left\{ \begin{array} { c c } \frac { 1 } { x - 11 } , & x \neq 11 \\9 , & x = 11\end{array} \right.$