Discuss the continuity of `f(x)={x{x}+1,0lt=x<1 and 2-{x},1lt=x<2` where `{x}` denotes the fractional part function.

Consider function f(x)={x{x}+1,\ \ \ \ \ \ \ \ \ \ \ \ 0lt=x<1 2-{x},\ \ \ \ 1lt=xlt=2\ \ \ where {x}: fractional part function of x . Statement-1: Rolles Theorem is not applicable to f(x) in [0,2] Statement-2: f(0)\ !=f(2)

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:

Discuss the continuity of the function f(x)={{:(2x -1 "," x lt 1),(3x-2"," x ge 1):}

Discuss the continuity of the function f(x)={x , 0lt=x<1//2 12 , x=1//2 1-x , 1//2

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

Discuss the continuity of the function f(x) ={(x", " x ge 0),(2", "x lt0):} at x=0

The area (in sq. units ) of the region A = { (x,y):(x - 1) [x] lt= y lt= 2 sqrtx , 0 lt= x lt= 2 ] where [t] denotes the greatest integer function is

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

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.