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^(2)} , where {x} denotes the fractional part of x , then

If f(x)={x^2}-({x})^2, where (x) denotes the fractional part of x, then

f(x)=sqrt((x-1)/(x-2{x})) , where {*} denotes the fractional part.

lim_(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part of x) is equal to

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]

let f(x)=(cos^-1(1-{x})sin^-1(1-{x}))/sqrt(2{x}(1-{x})) where {x} denotes the fractional part of x then

lim_(x->-1)1/(sqrt(|x|-{-x}))(w h e r e{x} denotes the fractional part of (x) ) is equal to (a)does not exist (b) 1 (c) oo (d) 1/2

If f(x)=1/(x^(2)+1) and g(x)=sinpix+8{x/2} where {.} denotes fractional part function then the find range of f(g(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