Let `f(x)` be real valued and differentiable function on `R` such that `f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y))` `f(0)` is equals a. 1 b. 0 c. -1 d. none of these

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(x) is Odd function Even function Odd and even function simultaneously Neither even nor odd

If f(x) is a real valued and differentaible function on R and f(x+y)=(f(x)+f(y))/(1-f(x)f(y)) , then show that f'(x)=f'(0)[1+t^(2)(x)].

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f(x) be real valued differentiable function not identically zero such that f(x+y^(2n+1)=f(x)+{f(y)}^(2n+1),nin Nandx,y are any real numbers and f'(0)le0. Find the values of f(5) andf'(10)

Let f(x) be a differentiable function on x in R such that f(x+y)=f(x). F(y)" for all, "x,y . If f(0) ne 0, f(5)=12 and f'(0)=16 , then f'(5) is equal to

If f is a real- valued differentiable function satisfying |f(x) - f(y)| le (x-y)^(2) ,x ,y , in R and f(0) =0 then f(1) equals

If f(x) is a differentiable real valued function such that f(0)=0 and f\'(x)+2f(x) le 1 , then (A) f(x) gt 1/2 (B) f(x) ge 0 (C) f(x) le 1/2 (D) none of these