The function `{:(f (x) =ax (x-1)+b, x lt 1),( =x-1, 1 le x le 3),( =px ^(2)+qx +2, x gt 3):}`
if (i) f (x) is continous for all x
(ii) ` f'(1)` does not exist
(iii) `f '(x)` is continous at `x=3,` then

Let f (x)= {{:(ac (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +qx +2,,, x gt 3):} is continous AA x in R except x =1 but |f (x)| is differentiable everywhere and f '(x) is continous at x=3 and |a+p+q|=k, then k=

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

The function f(x) = {(x+2, ",",1 le x lt 2),(4, ",", x = 2 ),(3x-2, ",", x gt 2 ):} is continuous at

If f(x)={(ax+3",",x le 2),(a^(2)x-1"," , x gt 2):} , then the values of a for which f is continuous for all x are

If f(x) ={(|x|,",",x lt 0),(x,",",0 le x le 1),(1,",",x gt 1):} , then f(x) is discontinuous at

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