Which of the following statements are correct?
(A) If $f: R \rightarrow R$ then $f(x)=|x|$ is continuous everywhere.
(B) If $f: R \rightarrow R$ then $f(x)=|x|$ is continuous everywhere but not differentiable at $x=0$.
(C) Let $f: R-\{0\} \rightarrow R$ then $f(x)=\frac{1}{x}$ is continuous everywhere.
(D) Let $f: R \rightarrow R$ then $f(x)=|x-1|+|x-2|$ is continuous everywhere but not differentiable at exactly 2 points.
(E) If $f: R \rightarrow R$ then $f(x)=\cot x$ is continuous everywhere.
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 3
A. → Correct as there is no discontinuity
B. → Correct
C. → Correct
D. → Correct
E → Incorrect as $\cot x = \frac{\cos x}{\sin x}$ so for sin x = 0 is discontinuous i.e. at $x = n\pi$ it is discontinuous