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

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 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

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

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

f(x) {(|x-(1)/(2)|",",0 le x lt 1),(x[x]",",1 le x lt 2):} where [.] denotes the greatest integer function. Show that f(x) is continuous at x=1 but not differentiable at x=1.

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)={{:(,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)

Lt_(xto2) [x] where [*] denotes the greatest integer function is equal to