Consider the function `f(x)=[x/([x]) if 1leq x leq 2 and if x=2 and sqrt(6-x) if 2 lt x leq 3` le where [x] denotes step up function then at `x = 2` function -

f(x) = 1 + [cosx]x in 0 leq x leq pi/2 (where [.] denotes greatest integer function) then

Let f(x)=1+x , 0 leq x leq 2 and f(x)=3−x , 2 lt x leq 3 . Find f(f(x)) .

Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The total number of points of discontinuity of f (x) for x in[-2,2] is:

Consider the function f(x) = [{:(x{x}+1",","if",0 le x lt 1),(2-{x}",","if",1 le x le 2):} , where {x} denotes the fractional part function. Which one of the following statements is not correct ?

Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The number of points for x in [-2,2] where f (x) is non-differentiable is:

Consider a function defined in [-2,2] f (x)={{:({x}, -2 lle x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The total number of points of discontinuity of f (x) for x in[-2,2] is:

Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}",","if",1 le x le 2):} , where {x} denotes the fractional part function. Which one of the following statements is not correct ?

Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}",","if",1 le x le 2):} , where {x} denotes the fractional part function. Which one of the following statements is not correct ?

If f(x)=sgn(x-2) xx [In x], 1leq x leq 3 and {x^2} ,-3 lt x leq 3.5 where [.] denotes the greatest integer function and {.} represents the fractional part functon, then the number of points of discontinuity in [1,3.5] is

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then (x) is continuous at x=2