Home
Class 12
MATHS
If f:R rarr R satisfying f(x-f(y))=f(f(y...

If `f:R rarr R` satisfying f(x-f(y))=f(f(y))+xf(y)+f(x)-1, for all `x,y in R`, then `(-f(10))/7` is ……… .

Text Solution

Verified by Experts

The correct Answer is:
7
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)

A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)| for all x,y in R. If f'(0) exists, prove that f'(x) exists for all x, in R.

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N such that f(1) = 3 and sum _(x=1)^nf(x)=120 , find the value of n.

If f is a function satisfying f(x+y)=f(x)xxf(y) for all x ,y in N such that f(1)=3 and sum_(x=1)^nf(x)=120 , find the value of n .

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a, (a)f(x) is a periodic function (b)f(x) is a constant function (c) f(x)=1/2 (d) f(x)=(cosx)/2

If f : R-{-1}->R and f is differentiable function satisfies " f (x+f(y) +x f(y)) = y+f(x)+y.f(x) for all x,y belongs to R-{-1} then find the value of 2010 [ 1 +f(2009)]

Let f : R rarr R satisfying |f(x)|le x^(2), AA x in R , then show that f(x) is differentiable at x = 0.

If f(x) is a differntiable function satisfying the condition f(100x)=x+f(100x-100), forall x in R and f(100)=1, then f(10^(4)) is