wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If f(x)=x,when0<x1/21,whenx=1/21x,when1/2<x<1 , then

A
f(x) is continuous for all real x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
f(x) is discontinuous for all real x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
f(x) is continuous only at x=12
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
f(x) is discontinuous only at x=12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C f(x) is continuous only at x=12
Let a be any real number
limxaf(x)=limxax=a ( when xa through rational values)
limxaf(x)=limxa(1x)=1a ( when xa through irrational values)
limxaf(x) will exist only when a=1a or a=12
Thus, if x12, then limx0f(x) will not exist and hence f(x) will be discontinuous at x=a
where a12
Also. limx0f(x)=12 and f(12)=12
Hence, f(x) is continuous at x=12

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Factorisation and Rationalisation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon