Q. 1035.0( 1 Vote )

State True or False for the statements

If f is continuous on its domain D, then |f| is also continuous on D.

Answer :

True

Given that, f is continuous on its domain D.


Let a be an arbitrary real number in D. Then f is continuous at a.



Now,


[ |f|(x) = |f(x)| ]




|f| is continuous at x=a.


Since a is an arbitrary point in D. Therefore |f| is continuous in D.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Super 10 Question: Check Your Knowledge of Maxima & Minima (Quiz)Super 10 Question: Check Your Knowledge of Maxima & Minima (Quiz)Super 10 Question: Check Your Knowledge of Maxima & Minima (Quiz)45 mins
Maxima & Minima in an intervalMaxima & Minima in an intervalMaxima & Minima in an interval60 mins
Questions Based on Maxima & MinimaQuestions Based on Maxima & MinimaQuestions Based on Maxima & Minima57 mins
Connection B/w Continuity & DifferentiabilityConnection B/w Continuity & DifferentiabilityConnection B/w Continuity & Differentiability59 mins
Questions based on Maxima & Minima in an intervalQuestions based on Maxima & Minima in an intervalQuestions based on Maxima & Minima in an interval59 mins
Check your Knowlege of Maxima & Minima ( Challenging Quiz)Check your Knowlege of Maxima & Minima ( Challenging Quiz)Check your Knowlege of Maxima & Minima ( Challenging Quiz)60 mins
Problems Based on L-Hospital Rule (Quiz)Problems Based on L-Hospital Rule (Quiz)Problems Based on L-Hospital Rule (Quiz)0 mins
When does a Maxima or Minima occur?When does a Maxima or Minima occur?When does a Maxima or Minima occur?48 mins
Interactive Quiz | Differentiability by using first principleInteractive Quiz | Differentiability by using first principleInteractive Quiz | Differentiability by using first principle59 mins
Interactive Quiz on LimitsInteractive Quiz on LimitsInteractive Quiz on Limits67 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses