`[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.

Prove that [x]+[y] le [x+y] , where x=[x]+{x} and y=[y]+{y} [*] represents greatest integer function and {*} represents fractional part of x.

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)

Solve the following equations (where [*] denotes greatest integer function and {*} represent fractional part function and sgn represents signum function)

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

The number of solution(s) integer function and ) of the equation [x]+2{-x}=3x, is/are (whhere (1 represents the greatest integer function and {x} denotes the fractional part of x)

Solve (1)/(x)+(1)/([2x])={x}+(1)/(3) where [.] denotes the greatest integers function and {.} denotes fractional part function.

Consider the function f(x) = {x+2} [cos 2x] (where [.] denotes greatest integer function & {.} denotes fractional part function.)