Let `f: R->R` satisfying `f((x+y)/k)=(f(x)+f(y))/k( k != 0,2)`.Let `f(x)` be differentiable on `R and f'(0) = a`, then determine `f(x)`.

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 : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in R. If f (x) is differentiable at x = 0, then

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

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.

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.

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.

A function f : R to R Satisfies the following conditions (i) f (x) ne 0 AA x in R (ii) f(x +y)= f(x) f(y) AA x, y, in R (iii) f(x) is differentiable (iv ) f'(0) =2 The derivative of f(x) satisfies the equation