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:

If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt x le 3):}, then

Let a function f(x) be defined in [-2, 2] as f(x) = {{:({x}",",, -2 le xlt -1), (|"sgn "x|",",,-1le x le 1),({-x}",",, 1 lt xle 2):} where {x} and sgn x denote fractional part and signum functions, respectively. Then find the area bounded by the graph of f(x) an the x-axis.

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 f (x) in [0,2pi] defined as : f(x)=[{:([sinx]+ [cos x],,, 0 le x le pi),( [sin x] -[cos x],,, pi lt x le 2pi):} where {.} denotes greatest integer function then. Number of points where f (x) is non-derivable :

Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x le 2):} and g(x)={([x]",",-pi le x lt 0),(sinx",",0le x le pi):} where [.] denotes the greatest integer function. The number of integral points in the range of g(f(x)) is

Consider two functions f(x)={([x]",",-2le x le -1),(|x|+1",",-1 lt x le 2):} and g(x)={([x]",",-pi le x lt 0),(sinx",",0le x le pi):} where [.] denotes the greatest integer function. The number of integral points in the range of g(f(x)) 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 continutity and diffrentiability of f(x)

f(x) {{:(-2"," if x le -1),(2x"," if -1lt x le 1),(2"," if x gt 1):}

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then