If the function `f(x)={(Ax-B ,, x le 1),(3x ,,1 lt x lt 2),(Bx^2-A ,, x ge 2):}`
is continuous at `x=1` and discontinuous at `x=2`,
find the values of `A and B`.

If the function f(x)={A x-B ,xlt=1 3x ,1

The function f(x)= {(5x-4 ", " 0 lt x le 1 ),( 4x^3-3x", " 1 lt x lt 2):}

Show that the function f(x) = {{:(2x+3",",-3 le x lt -2),(x+1",",-2 le x lt 0),(x+2",",0 le x le 1):} is discontinuous at x = 0 and continuous at every point in interval [-3, 1]

Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 ),(" "37 - x," "2 lt x le 3 ):} is continuous at x = 2

If the function f(x)= {(3ax +b", " x gt 1 ),(11 ", "x=1),(5 ax-2b", " x lt 1):} continuous at x= 1 then ( a, b) =?

Show that the function f(x)={:{(1-x", " x lt1),(x^2-1 ", " x ge 1):} is continuous but not differnetiable at x=1

For what value of k, the function f(x) ={:{(2x+1", "x gt2),(" "k ", " x=2),(3x-1 ", "x lt2):}, is continuous at x=2.

Examine the function, f(x) = {{:(x - 1",",x lt 0),(1//4",",x = 0),(x^(2)-1",",x gt 0):} Discuss the continuity and if discontinuous remove the discontinuity.

A function f(x) is defind as f(x)={{:(x^(2)+ax+1, " x is rational "),(ax^(2)+2x+b,"x is irrational "):} is continuous at x=1and 3 , them find the values of a and b.

Discuss the continuity of the function f(x)={{:(2x -1 "," x lt 1),(3x-2"," x ge 1):}