The number of function `f:[0,1] to [0,1]" satisfying " |f(x)-f(x)|=|x-y| " for all "x, y " in " [0,1] is`

There exists a function f(x) satisfying f(0)=1, f'(0)=-1, f(x) gt 0 , for all x, then :

If f is a real valued difrerentiable function satisfying | f (x) - f (y) | le (x -y) ^(2) for all, x,y in RR and f(0) =0, then f(1) is equal to-

Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) for all x, y in R and f(0) = 0 , then for any n in N , f(n) =

Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) for all x, y in R and f(0) = 0 , then for any n in N , f(n) =

If f is a real valued differentiable function satisfying | f (x) - f (y) | le (x - y) ^(2) for all real x and y and f (0) =0 then f (1) equals :

There exists a function f(x) satisfying 'f (0)=1,f(0)=-1,f(x) lt 0,AAx and

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is