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

If f:(0,)(0,) satisfy

f(xf(y))=x2y2(aR),then

nr=1f(r)nCr is


A

n.2n1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

n(n1)2n2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

n.2n1+n(n1)2n2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

n.2n1+n(n1)2n2


Taking x = 1

f(f(y))=ya

Let f(y)=1xf(1)=1(f(y))2ya..............(i)

and Let y=1

(f(1))3=1f(1)=1

Now use y=1

then f(x)=x2

So from (1)(f(y))2=yay4=yaa=4

(A) is true

nr1f(r)nCr=nr1r2

nCr

nr1(r(r1)+1)

nCr

=n(n1)2n2+n.2n1

(C ) is true.


2f(x)=ex

2x2ex

3 solutions

(C) is true.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Methods of Solving First Order, First Degree Differential Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon