Let `f: RR rarr RR` such that for all `'x' and y` in `RR,\ |f(x) - f(y)| lt= |x-y|^3` then `f(x)` is

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 f: RR rarr RR be a function defined by f(x)=ax+b , for all x in RR . If (f o f)=I_(RR) Find the value of a and b.

Let F : R to R be such that f is injective and f(x) f(y) =f(x+y) for all x,y in RR If f(x) , f(y) , f(z) are in G.P ., then x,y,z are in -

Let RR be the set real numbers and f: RR rarr RR be given by f(x) =ax +2 , for all x in RR . If (f o f) =I_(RR) , find the value of a

Let a, b in RR and f : RR rarr RR be defined by f(x) = a cos(|x^3-x|) + b|x| sin(|x^3+x|). Then f is

Let RR be the set of real numbers . If the functions f:RR rarr RR and g: RR rarr RR be defined by , f(x)=3x+2 and g(x) =x^(2)+1 , then find ( g o f) and (f o g) .

Let f RR rarr RR be differentiable at x = 0 . If f(0) = 0 and f'(0) = 2, then the value of underset(x rarr 0)lim (1)/(x)[f(x) + f(2x) + f(3x)+…+f(2015x)] is

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

Let RR be the set of real numbers and f: RR rarr RR ,g: RR rarr RR be two functions such that, (g o f) (x) = 4x^(2)+4x+1 and (f o g ) (x) = 2x^(2)+1 . Find f(x) and g(x) .