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

If f(x - y) ,f(x) f(y) and f(x + y) are in A.P for all x, y R and f (0) 0 then-


A

is an even function

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

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

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

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

The correct options are
A

is an even function


B


2 f (x) f(y) = f (x - y) + f ( x + y) at x = y = 0 ; f (0) = 1 ( f (0) 0 )

and at y = 0

2 f (x) = f (- x) + f (x) f (x) = f ( - x)

ie . f (x) is an even function f(x) = - f ( - x)

f (1) + f (-1) = 0

Also f(x) = - f (- x)

f(x) + f (- x) = 0


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