It `f:Z to Z` be a function defined by `f(x+y)=f(x)+f(y)` for all `x,y epsilon R` show that `f(x)=xf(1)` for all `x epsilon R`.

Let f : R to R be a function given by f(x+y) = f(x) + f(y) for all x,y in R such that f(1)= a Then, f (x)=

Let f:R rarr R be a function given by f(x+y)=f(x)f(y) for all x,y in R .If f'(0)=2 then f(x) is equal to

Let f : R to R be a function given by f(x+y)=f(x)f(y) for all x , y in R If f(x) ne 0 for all x in R and f'(0) exists, then f'(x) equals

Let f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)

Let f:R to R be a function satisfying f(x+y)=f(x)+f(y)"for all "x,y in R "If "f(x)=x^(3)g(x)"for all "x,yin R , where g(x) is continuous, then f'(x) is equal to

Let f:R to R be a function given by f(x+y)=f(x) f(y)"for all "x,y in R "If "f(x)=1+xg(x),log_(e)2, "where "lim_(x to 0) g(x)=1. "Then, f'(x)=

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

Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

If a real valued function f(x) satisfies the equation f(x+y)=f(x)+f(y) for all x,y in R then f(x) is