If `f(x+y,x-y) =xy`, then the arithmetic mean of `f(x,y)` and `f(y,-x)` is

A

x

B

y

C

0

D

1

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

If f(2x + 3y, 2x-3y)=4xy , then find the value of f(x,y)

If f(2x+3y, 2x-7y)=20x , then f(x, y) equals

If f(2x + y/8 , 2x - y/8) = xy , then f(m,n)+f(n,m)=0

If f(0) = 0 , f '(0) = 2 , then the derivative of y = f(f(f(f(x)))) at x = 0 in

If y=f(x)=(2x-1)/(x-2), then f(y)=

f(x - y), f(x) f(y), f(x + y) are in A.P. AA x, y and f(0) != 0 then

If y=f(x) =(x+2)/(x-1)(x ne 1,-2) then show that x=f(y)

y = f(x) , Where f satisfies the relation f(x + y) = 2f(x) + xf(y) + ysqrt(f(x)) AA x, y in R and f'(0) = 0 . Then f(6) is equal to ………

If f(x) satisfies the relation f(x+ y) = f ( x) + f( y ) for all x, y in R and f(1) = 5 then

If f(x+y)=f(xy)AAx,y in R then prove that f is a constane function.