Let `f(x)={{:(2x+1,"when "xlt2),(k+2,"when "x=2),(4x-3,"when "xgt2):}` Find the value of k for which f (x) is continuous at x = 2 .

A continuous function f(x) is defined as follows : f(x)={{:(x,"when "xlt1),(ax+bx^(2),"when "1lexle2),(2x^(2),"when "xgt2):} Find the values of a and b.

A function f (x) is defined as follows: f(x)={{:(x^(4)-3,"when " xle2),(x^(3)+5,"when "xgt2):} Prove that the function f (x) is continuous at x = 2 .

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.

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

f(x)={{:(3k-2x", when "xlt1),(2k+1", when "xge1):} at x = 1

A function f (x) is defined as follows: f(x)={{:(x+2,"when "xlt2),(x^(2)-1,"when "xge2):} Show that f (x) is discontinuous at x = 2 and the jump of the function at this point is -1 .

Let f(x)={[(x-1)^((1)/(2-x)),x>1,x!=2 , [k,x=2] .The value of k for which f is continuous at x=2 is

If the function defined by : f(x)={{:(2x-1", "xlt2),(a", "x=2),(x+1", "xgt2):} is continuous at x = 2, find the value of 'a'. Also discuss the continuity of f(x) at x = 3.