CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let f(x) = x - |x| then f(x) is,
  1. Continuous × R

  2. discontinuous at x = 0

  3. Always increasing

  4. a constant


Solution

The correct option is A

Continuous × R


Given function is,
f(x)=x|x|
when x>0
f(x)=xx=0
when x<0
f(x)=x(x)
=2x

The graph for the above can be represented as below.

This shows that no breakage is happening at any point including at x = 0. That is the function is continuous at every point x ϵ R.

Also its not strictly increasing since in x> 0 the function is constant, that is nor then increasing nor decreasing.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
QuestionImage
QuestionImage
View More...


People also searched for
QuestionImage
QuestionImage
View More...



footer-image