If `f(x)={:{(1+sin x", " 0 le x lt pi//2),(" "1 ", " x lt0):}` then show that f'(0) does not exist.

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

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

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

Let a function f be defined as f(x) = {:{(x," if " 0 le x lt 1/2),(0," if "x=1/2),(x-1," if" 1/2 lt x le 1):} Establish the existence of Lim_(x to 1/2) f(x) .

Let f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):} Then f(x) is

If f(x) is defined as follows: f(x)={{:(1,x,gt0),(-1,x,lt0),(0,x,=0):} Then show that lim_(xrarr0) f(x) does not exist.

f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):} Discuss the continuity

Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f ^(-1) (x) is discontinous at x=

If f (x)= [{:(e ^(x-1),,, 0 le x le 1),( x+1-{x},', 1 lt x lt 3 ):}and g (x) =x ^(2) -ax +b such that f (x)g (x) is continous [0,3] then the ordered pair (a,b) is (where {.} denotes fractional part function):

If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) is not differentiable at: