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).

If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

A function f (x) is defined as follwos : f(x){:(=2x+1," when "xle 1),(= 3-x," when "xgt1):} Examine whether underset(xrarr1)"lim"f(x) exists or not.

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 .

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+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)={{:(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 function f (x) is defined as follows : f(x)={{:(3x+1,"for "xle1 ),(3-ax^(2),"for " xgt1):} If f (x) is continuous at x = 1 , find the value of a.

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.

A function f(x) is defined as follows : " "f(x)={:{(x-1",","when "x gt 0),(-(1)/(2)",","when "x = 0),( x+1",","when "xlt0):} Draw the graph of the function f(x). From the graph find the value of f(x) at x=-(1)/(2) and examine whether f(x) is continuous at x = 0.

A function is defined as f(x) = {(e^x, xle0),(|x-1|, x gt0):} , then f(x) is