" If "f(x)={[(x^(2)-1)/(x+1)," when "x!=-1," then "],[-2," when "x=-1]

Let f(x) = {((x^(2) -2x -3)/(x + 1)","," when " x != -1),(" k,"," when " x = -1):} If f(x) is continuous at x = -1 then k = ?

If f(x)={(x-2)/(x^(2)-3x+2), when x!=21 when x=2, prove that f'(2)=-1

A function f(x) is defined as follows : f(x)=x," when "x lt1 =x+1," when "x gt1 =3/2," when "x=1 Draw the graph of f(x) and examine its continuity at x=(1)/(2)and x=1.

If f(x) = {(x^(2), ",","when" x != 1),(2,",","when" x = 1):} , then

If f(x) = {(x^(2), ",","when" x != 1),(2,",","when" x = 1):} , then

Find the value of k for which f(x)={{:((x^(2)-2x-3)/(x+1)",","when",x ne-1, ),(lambda",", "when", x =-1):} is continuous at x =-1

The definition of the function f (x) is given below: f(x)={{:((1)/(2)-x,"when "xlt3 ),(1,"when " x=3),(x-(1)/(2),"when " xgt3):} Calculate f (3-0), f(3+0),f(3) and state whether f (x) is continuous at x =3 or not.

If f(x) ={{:((x-1)/(2x ^(2) -7x +5),"when"x ne1),(-1/3, "when" x=1):} then the value of f '(1) is-

If f(x) = {((|x-a|)/(x-a), ",","when"x != a),(1, ",", "when"x = a ):} , then

If f(x) = {((|x-a|)/(x-a), ",","when"x != a),(1, ",", "when"x = a ):} , then