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)

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

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

If f(x)=([x])/(|x|), x ne 0 , where [.] denotes the greatest integer function, then f'(1) is

If f(x)=([x])/(|x|),x ne 0 where [.] denotes the greatest integer function, then f'(1) 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 A. f(x) is continuous for all x in [0, 2) B. f(x) is differentiable for all x in [0, 2) - {1} C. f(X) is differentiable for all x in [0, 2)-{(1)/(2),1} D. None of these

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 [.] denotes the greatest integer function, then f(x)=[x]+[x+(1)/(2)]

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

Draw the graph of the function f(x) = x-|x2-x| -1 le x le 1 , where [*] denotes the greatest integer function. Find the points of discontinuity and non-differentiability.