If `f(x)=(2^({x})-1)/(2^({x})+1)` then (where {x} represent fractional part of x) `D_f in R` (b) `R_f in [0,1/3)` period of `f(x)` is 1 (d) `f(x)` is even function

If domain of f(x) is (-oo,0) , then domain of f(6{x}^2-5(x)+ 1) is (where {.} represents fractional part function)

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 int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c , then (a) f(x) is an even function (b) f(x) is a bounded function (c) the range of f(x) is (0,1) (d) f(x) has two points of extrema

The domain of definition of the function f(x)={x}^({x})+[x]^([x]) is where {dot} represents fractional part and [dot] represent greatest integral function). (a) R-I (b) R-[0,1] R-{Iuu(0,1)} (d) Iuu(0,1)

Let f(x) = ([x]+1)/({x}+1) for f: [0, (5)/(2) ) to ((1)/(2) , 3] , where [*] represents the greatest integer function and {*} represents the fractional part of x. Draw the graph of y= f(x) . Prove that y=f(x) is bijective. Also find the range of the function.

If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is 1 (b) 2 (c) 3 (d) 4

If f:R rarr R is a function such that f(5x)+f(5x+1)+f(5x+2)=0, AA x in R , then the period of f(x) is

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :