Let f be a function satisfying f(x+y)=f(...

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

`k^(n)`

B

nk

C

k

D

None of these

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

f(xy)=f(x)+f(y) is true for all

Let f(x) be 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)^(n) f(x) = 120 . Then the vlaue of n is :

If f:RtoR satisfies f(x+y)=f(x)+f(y) for all x,yinRandf(1)=7 , then sum_(r=1)^(n)f(r) is :

If f(x) 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)^(n) f(x) = 120 Then the value of n is :

If f(x+y) = 2f(x) f(y) for all x,y where f^(')(0) = 3 and f(4) =2, then f^(')(4) is equal to

Let f be function satisfying f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x) , for all x and y, where g(x) is a continuous function. Then f'(x) is :

There exists a function f(x) satisfying f(0)=1, f'(0)=-1, f(x) gt 0 , for all x, then :

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

If f(x) is a ploynomial function satisfying f(x) . f(1/x) = f(x) + f(1/x) and f(3)=28, then f(2) is

Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x and f(0)=3 The value of f(x).f(-x) for all x is