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

Draw the graph of y={|x|} , where {.} represents the fractional part function.

Draw the graph of |y|={x} , where {.} represents the fractional part function.

f(x)={[sinpix],0lt=x<1sgn(x-5/4)x{x-2/3},1lt=xlt=2 where [.] denotes the greatest integer function and {.} represents the fractional part function. At what points should the continuity be checked? Hence, find the points of discontinuity.

Solve : 4{x}= x+ [x] (where [*] denotes the greatest integer function and {*} denotes the fractional part function.

Draw the graph of y= 2^({x}) , where {*} represents the fractional part function.

Draw the graph of f(x) ={2x} , where {*} represents the fractional part function.

Draw the graph of y=|{x}-0.5| , where {.} represents the fractional part function.

Solve : x^(2) = {x} , where {x} represents the fractional part function.

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.

Find the domain and range of f(x)=log{x},w h e r e{} represents the fractional part function).