Question -
Answer -
The given function┬аf┬аis┬а
┬а
Thegiven function┬аf┬аis defined at all the points of the realline.
Let┬аc┬аbea point on the real line.
Case I:
Therefore,┬аf┬аiscontinuous at all points┬аx, such that┬аx┬а< 1
Case II:
If┬аc┬а=1, then the left hand limit of┬аf┬аat┬аx┬а= 1 is,
Theright hand limit of┬аf┬аat┬аx┬а= 1 is,
It isobserved that the left and right hand limit of┬аf┬аat┬аx┬а=1 do not coincide.
Therefore,┬аf┬аisnot continuous at┬аx┬а= 1
Case III:
Therefore,┬аf┬аiscontinuous at all points┬аx, such that┬аx┬а> 1
Thus,from the above observation, it can be concluded that┬аx┬а= 1 isthe only point of discontinuity of┬аf.