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.

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

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

Let f:R rarr R such that for all x' and y in R,backslash|f(x)-f(y)|<=|x-y|^(3) then f(x) is

Let R be the set of all real numbers. If , f : R to R be a function such that |f (x) - f (y) | ^(2) le | x -y| ^(3), AA x, y in R, then f'(x) is equal to a)f (x) b)1 c)0 d) x ^(2)

Let R be the set of all real numbers. Let f: R rarr R be a function such that : |f(x) - f(y)|^2 le |x-y|^2, AA x, y in R . Then f(x) =

(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.