CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Let f:[0,)[2,) be a differentiable increasing and onto function satisfying f2(x)2f(x)x=f2(y)2f(y)y
If g(x) be the inverse of f(x), then g(4) is

A
16
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
116
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
96
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
196
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 96
2f(x)f(x)2f(x)12x=0
2(f(x)1)f(x)=12x
Integrating both the sides
(f(x)1)2xC=0
f(0)=2C=1
f(x)=1+x+1
g(x) is inverse of f(x)
Let f(x)=y
(y1)2=x+1((y1)21)2=xg(x)=((x1)21)2g(x)=2((x1)21)×2(x1)g(4)=96

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