If `[.]` and `{.}` are greatest integer and fractional part functions, then the maximum value of `f(x)=sqrt(x-[{x}]-2018)+sqrt(2020-x+{[x]})` is

If[.] and {.} denote greatest integer and fractional part functions respectively, then the period of f(x) = e^(sin 3pi{x} + tan pi [x]) is

Find the domain and range of the following functions.(Read the symbols [*] and {cdots} as greatest integers and fractional part function respectively f(x)=cos^(-1)((sqrt(2x^(2)+1))/(x^(2)+1))

If f(x)=x+{-x}+[x] , where [x] and {x} denotes greatest integer function and fractional part function respectively, then find the number of points at which f(x) is both discontinuous and non-differentiable in [-2,2] .

If [.] denotes the greatest integer function and {.} denotes the fractional part,then the domain of the function f(x)=sqrt((x-1)/(x-{x}))+ln(3-[x+[2x]]) is

If [1 denotes the greatest integer and {} denotes the fractional part,then the domain of the real valued function f(x)=(f(x))/(sqrt(1000x^(2)-999(x)^(3)-990(x)^(2)-50x+60)) is

f(x) = {{:(1 + cos^(-1){cot x} " ," x Where [ ] denotes greatest integer and { } denotes fractional part function, Then value of jump of discontinuity is:

Solve : [x]^(2)=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively.

If f(x)=[x^(2)]+sqrt({x}^(2)), where [] and {.} denote the greatest integer and fractional part functions respectively,then