The function f(x) = x is discontinuous on the set

We know that, f(x) = x is continuous in R - n :n Z . Since, f(x) = x = x [ , x = 0 , ,n ,n Z] Hence, f(x) = x is discontinuous on the set x = n :n Z .

Continuity and Differentiability — Class 12 Maths Solution

exemplar objective MCQ NCERT Exemp. Ex.5.3 ,Q.86,Page 114

Question

The function $f(x) = \cot x$ is discontinuous on the set

(a) $\{ x = n\pi :n \in Z\}$
(b) $\{ x = 2n\pi :n \in Z\}$
(c) $\left\{ {x = (2n + 1)\frac{\pi }{2};n \in Z} \right\}$ ✓ Correct
(d) $\left\{ {x = \frac{{n\pi }}{2};n \in Z} \right\}$

Step-by-step Solution

We know that, $f(x) = \cot x$ is continuous in $R - \{ n\pi :n \in Z\}$.
Since, $f(x) = \cot x = \frac{{\cos x}}{{\sin x}}$ $[{\rm{since}},\sin x = 0\,{\rm{at}}\,n\pi ,n \in Z]$

Hence, $f(x) = \cot x$ is discontinuous on the set $\{ x = n\pi :n \in Z\}$.

← All Continuity and Differentiability solutions Practice tests →

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Continuity and Differentiability. Curated by Sachin Sharma. Free for all students.