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

The number of points at which the function f(x)={[cosπx],0x1|x1|[x2],1<x2
is discontinuous, is
([.] denotes the greatest integral function )

A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 4
For x=0,f(x)=1
For 0<x12,f(x)=0
For 12<x1,f(x)=1

For x(1,2),
[x2]=1 and |x1|=x1

For x=2, [x2]=0

f(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪1,x=00,0<x121,12<x1(x1),1<x<20,x=2

Clearly, f is discontinuous at four points i.e., {0,12,1,2} in the interval [0,2]

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Types of Discontinuity
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon