If `f^(prime)(x)=|x|-{x},` where {x} denotes the fractional part of `x ,` then `f(x)` is decreasing in (a) `(-1/2,0)` (b) `(-1/2,2)` `(-1/2,2)` (d) `(1/2,oo)`

If f'(x)=|x|-{x} where {x} denotes the fractional part of x, then f(x) is decreasing in (-1/2, k) , find k.

Period of f(x)=cos2pi{x} is , where {x} denote the fractional part of x)

If f(x)={(sin{cosx}/(x-pi/2), x ne pi/2),(1, x=pi/2):} , where {.} denotes the fractional part of x, then f(x) is :

The domain of f(x)=sqrt(2{x}^2-3{x}+1), where {.} denotes the fractional part in [-1,1] is (a) [-1,1]-(1/(2),1) (b) [-1,-1/2]uu[(0,(1/2)]uu{1} (c) [-1,1/2] (d) [-1/2,1]

If f: [2,3) rarr [0,1) is defined by f(x)=x-[x] , the fractional part of x, then f^-1(x)

Let f(x)=sqrt(|x|-{x})(w h e r e{dot} denotes the fractional part of (x)a n dX , Y are its domain and range, respectively). Then (a) X in (-oo,1/2) and Y in (1/2,oo) (b) X in (-oo in ,1/2)uu[0,oo)a n dY in (1/2,oo) (c) X in (-oo,-1/2)uu[0,oo)a n dY in [0,oo) (d) none of these

lim_(x->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x (a) e^2−7 (b) e^2−8 (c) e^2−6 (d) none of these

If 2f(x)+f(-x)=1+x,find f'(10),where f'(x) denote derivative of f(x).

The period of function 2^({x})+sinpix+3^({x/2})+cos2pix (where {x} denotes the fractional part of (x) is 2 (b) 1 (c) 3 (d) none of these

If 2f(x)+f(-x)=1+x" find "f'(10) where f'(x) denote derivative of f(x).