`[2x]-2[x]=lambda` where [.] represents greatest integer function and {.} represents fractional part of a real number then

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.

The set of all values of x satisfying {x}=x[xx] " where " [xx] represents greatest integer function {xx} represents fractional part of x

FInd lim_(x->alpha^+) [(min (sin x, {x}))/(x-1)] where alpha is the root of the equation sinx+1 =x Here [.] represents greatest integer function and {.} represents fractional part function

lim_(xrarrc)f(x) does not exist for wher [.] represent greatest integer function {.} represent fractional part function

Sum of all the solution of the equation ([x])/([x-2])-([x-2])/([x])=(8{x}+12)/([x-2][x]) is (where{*} denotes greatest integer function and {*} represent fractional part function)

Let [.] represent the greatest integer function and f (x)=[tan^2 x] then :

If f(x)={x}+{x+[(x)/(1+x^(2))]}+{x+[(x)/(1+2x^(2))]}+{x+[(x)/(1+3x^(2))]}.......+{x+[(x)/(1+99x^(2))]} , then values of [f(sqrt(3))] is where [*] denotes greatest integer function and {*} represent fractional part function)

The number of points of discontinuity of f(x)=[2x]^(2)-{2x}^(2) (where [ ] denotes the greatest integer function and { } is fractional part of x) in the interval (-2,2) , is

Solve the following equation (where [*] denotes greatest integer function and {*} represent fractional part function ) [x^(2)]+2[x]=3x , 0 le x le 2 .

f(x)= {cos^(-1){cotx) ,x pi/2 where [dot] represents the greatest function and {dot} represents the fractional part function. Find the jump of discontinuity.