[" 7) If "f(x+y)=f(y)+x,y in R" then "],[" prove that "f" is a constant function."]

If f(x+y)=f(xy)AAx,y in R then prove that f is a constane function.

(i) if f ( (x + 2y)/3)]= (f(x) +2f(y))/3 , " x, y in R and f (0) exists and is finite ,show that f(x) is continuous on the entire number line. (ii) Let f : R to R satisfying f(x) -f (y) | le | x-y|^(3) , AA x, y in R , The prove that f(x) is a constant function.

(i) if f ( (x + 2y)/3)]= (f(x) +2f(y))/3 , " x, y in R and f (0) exists and is finite ,show that f(x) is continuous on the entire number line. (ii) Let f : R to R satisfying f(x) -f (y) | le | x-y|^(3) , AA x, y in R , The prove that f(x) is a constant function.

If (x).f(y)=f(x)+f(y)+f(xy)-2AA x,y in R and if f(x) is not a constant function,the value of f(1) is equal to

If f(x+y)=f(x)*f(y) for all real x,y and f(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^(2)) is an even function.

Let f be a function defined on R such that f(x + y) = f (x) + f(y) AA x,y in R . If is continuous at x = 0 , Prove that it is continuous on R .

Let R be the set of real numbers and f : R to R be such that for all x and y in R, f(x) -f(y)|^(2) le (x-y)^(3) . Prove that f(x) is a constant.

Let R be the set of real numbers and f : R to R be such that for all x and y in R, |f(x) -f(y)|^(2) le (x-y)^(3) . Prove that f(x) is a constant.

If f(x+f(y))=f(x)+y for all x,y in R and f(1)=1, then find the value of f(10)/5,f(x) is not constant function.