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 .

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 .

3.A function f(x) is defined as follows: f(x)={3+2x-(3)/(2) =(3)/(2) Show that f(x) is continuous at x=0 and discontinuous at x=3/2

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

f(x)={{:(2-x",","when",x lt2 ),( 2+x",", "when",xge2):} is discontinuous at x =2

3.A function f(x) is defined as follows f(x)=3+2x for -(3)/(2) =(3)/(2) show that f(x) is continuous at x=0 and discontinuous at x=(3)/(2)

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

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.

Show that the function f(x)={{:(x+(x+2)/(|x+2|),"when " xne-2),(" "-1,"when " x=-2):} is dicontinuous at x=-2 Also find the jump of f (x) at this point of discontinuity.

A function F(x) is defined as follows: F(x)={:{(1+2x,"when "xle1),(3-2x,"when "x gt1):} Determine F(0), F(-1.5),F(1), F(2.6) and F(x+2).

Let f(x)={{:(x^(3)-3x+2,"where "xlt2),(x^(3)-6x^(2)+9x+2,"where "xge2):} . Then-