`f(x)={{:(3-x",","when",x le0, ),( x^(2)",", "when",xgt0):}` is discontinuous at x=0

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

Show that the funcation f(x)={{:(3x-2",", " when ", x le0),(x+1",", " when ", x gt 0):} is discontinuous at x =0

f(x)={{:((sin3x)/(x)",","when",x ne0 ),( 1",", "when",x=0):} is discontinuous atx =0.

Show that the function f(x)={{:(x/|x|",", " when ", x ne0),(1",", " when ", x =0):} is discontinuous at x=0

f(x)={{:(2x",","when",x lt0, ),(2",", "when", x =2),(x^(2)",","when",xgt2):} is discontinuous at x=0

f(x)={{:(-x",","when",x lt0, ),(1",", "when", x =0),(x",","when",xgt0):} is discontinuous at x = 0

If the function f (x)= {{:(e ^(2x) -1",","when " x le 0),(ax+ (bx^(2))/(2)",","when " xgt0):} is differentiable at x=0 then-

Prove that, q(x) = {(|x|/x, when x ne 0),(0, when x = 0):} is discontinuous at x = 0.

Show that the function f(x) given by f(x)={((e^(1/x)-1)/(e^(1/x)+1), when x!=0), (0, when x=0):} is discontinuous at x=0 .

Consider the real function f:RtoR , defined by f(x)={{:(1-x",""when "xlt0),(1",""when "x=0),(x+1",""when "xgt0):} Write its domain and range. Also, draw the graph of f(x).