CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Let g(x) = {xx1x+1x1 and f(x) = {1xx0x2x0

Consider the composition of f and g. i.e, (f g)(x) -f(g(x)). The number of discontinties is (f g)(x) present in the interval (-,0) is.

A
0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 0
g(x) = {xx1x+1x1

f(x) = {1xx0x2x0

f g(x) = f(g(x)) = {1g(x),g(x)0(g(x))2,g(x)0

=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪1(x)x0,x11(x+1),x+10,x1(x)2x>0,x1(x+1)2,x+1>0,x1

= 1+x,0x1x2x<0(x+1)2x>1

f(g(x)) = x2x<0x+1,0x1(x+1)2x>1

f g(x) is continuous at every point in (-, 0).

Number of points of discontinuities = 0

Overall we have two points of discontinuities at x = 0 and x = 1 but these do not belong to the given interval (-, 0).

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Property 2
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon