Let ` f(x) = {{:(( 2+x)",",if , x ge0), (( 2-x)",", if , x lt 0):}` show that f(x) not derivable at x =0

If f(x)={:{(x", for " x ge 0),(x^(2)", for " x lt 0):} , then f is

If f(x)={(x^(2)",","for "x ge0),(x",","for "x lt 0):} , then fof(x) is given by

If f(x) = {(x,",", x ge 0),(x^(2),",",x lt 0):} , then f(x) is

let f(x) = {:{( x^(2) , x le 0) , ( ax , x gt 0):} then f (x) is derivable at x = 0 if

Let f(x)= {:{ (x + a , x ge 1 ) , ( ax^(2) + 1, x lt 1) :} then f(x) is derivable at x =1 , if

If f(x)={{:(2+x",", x ge0),(4-x",", x lt 0):}, then f (f(x)) is given by :

Let f (x) = {{:((1+sin x )",", when, 0 le x lt (pi)/(2)), (" " 1",", when, x lt 0 ):} Show that f ' (0) does not exist.

Let f(x)={{:(cosx, if ,x ge 0), (x+k, if ,x lt 0.):} Find the value of the constant k, given that lim_(x to 0)f(x) exists.

f(x)={{:(cosx",","when",x ge0, ),(-cosx",", "when", x lt0):} is discontinuous at x =0