Question

The function $f\left(x\right)=\{\begin{array}{ccc}5& when& 0<x<1\\ 8& when& 1<x<2\\ 15& when& 2<x\le 3\end{array}$is discontinuous

• A. at $x=1,2$
• B. at $x=4$
• C. at $x=0$
• D. at $x=3$

Answer 1

Answer: (A)

at $x=1,2$

Since, the domain has already been divided into 3 parts, we just concentrate on the critical points.

The critical points are x = 1 and x = 2

At x = 1

LHL = $\underset{x\to 1^{-}}{Lim}f\left(x\right)$ = 5

RHL = $\underset{x\to 1^{+}}{Lim}f\left(x\right)$ = 8

Since, the LHL is not equal to RHL at x= 1, the function is discontinuous at x = 1

At x = 2

LHL = $\underset{x\to 2^{-}}{Lim}f\left(x\right)$ = 8

RHL = $\underset{x\to 2^{+}}{Lim}f\left(x\right)$ = 15

Since, the LHL is not equal to RHL at x= 2, the function is discontinuous at x = 2

Thus the function is discontinuous at x = 1 and x = 2