Let `f:RR->RR` be a function such that `|f(x)-f(y)|<=6|x-y|^2` for all `x,y in R`. if `f(3)=6` then `f(6)` equals`:`

Let f:RR to RR,g:RR to RR and h:RR to RR be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(g(x)))=x for all x in RR . 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

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) .

Let f:RR rarr RR and g: RR rarr RR be two functions such that (g o f) (x) = sin ^(2) x and ( f o g) (x) = sin (x^(2)) . Find f(x) and g(x) .

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:RR rarr RR be the function defined by f(x)=x+1 . Find the function g:RR rarr RR , such that (g o f)(x)=x^(2)+3x+3

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 the function f:RR rarr RR be defined by , f(x)=4x-3 .Find the function g:RR rarr RR , such that (g o f) (x)=8x-1

If f: RR^(+) rarr RR ^(+) is a polynomial function satisfying the functional equation f{f(x)}=6x-f(x) , then f(17) is equal to ___