If `f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):}`, where [] denotes the greatest integer function, then

If f(x)= {(|1-4x^2|,; 0 lt= x lt 1), ([x^2-2x],; 1 lt= x lt 2):} , where [.] denotes the greatest integer function, then 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

If f(x) = {{:("sin"(pix)/(2)",",x lt 1),([x]",",x ge 1):} , where [x] denotes the greatest integer function, then

Let f(x)=(x^(2)+1)/([x]),1 lt x le 3.9.[.] denotes the greatest integer function. Then

Discuss the continuity of f(x) in [0, 2], where f(x) = {{:([cos pi x]",",x le 1),(|2x - 3|[x - 2]",",x gt 1):} where [.] denotes the greatest integral function.

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 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 ?

Let f : [-1, 3] to R be defined as {{:(|x|+[x]", "-1 le x lt 1),(x+|x|", "1 le x lt 2),(x+[x]", "2 le x le 3","):} where, [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at

Let f(x)=(x^(2)+2)/([x]),1 le x le3 , where [.] is the greatest integer function. Then the least value of f(x) is

If f(x) = {{:({x+(1)/(3)}[sin pi x]",",0 le x lt 1),([2x]sgn(x - (4)/(3))",",1 le x le 2):} , where [.] and {.} denotes greatest integerd and fractional part of x respectively, then the number of points, which is not differentiable, is