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 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

(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.

Let R be the set of real numbers and f:R rarr R be given by,f(x)=x^(2)+2. Find f^(-1){11,16}

Let R be the set of all real numbers let f: R to R : f(x) = sin x and g : R to R : g (x) =x^(2) . Prove that g o f ne f o g

Let R be the set of all real numbers and f : R rarr R be given by f(x) = 3x^(2) + 1 . Then the set f^(-1) ([1, 6]) is

Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(xy+1)=f(x)f(y)-f(y)-x+2. Then f is

Let R^(+) be the set of all positive real numbers. Let f : R^(+) to R^(+) : f(x) =e^(x) for all x in R^(+) . Show that f is invertible and hence find f^(-1)