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

Examine the continuity of the function f(x)={3x-2,xlt=0x+1,x >0"a t"x=0 Also sketch the graph of this function.

Discuss the continuity of the function f(x)={x , 0lt=x<1//2 12 , x=1//2 1-x , 1//2

Consider the function f(x)={2x+3,xlt=1-x^2+6,x >1

The value of b for which the function f(x)={5x-4,0xlt=1 , 4x^2+3b x ,1< x <2 and continuous at x=1

Find the complete set of values of alpha for which the function f(x) = {(x+1,xlt1 alpha , x =1 , is strictly increasing x=1 x^(2)-x+3,xlt1

Find the points of discontinuity, if any, of the following function: f(x)={-2 , if xlt=-1 2x , if-1

Let a and b are real numbers such that the function f(x)={(-3ax^(2)-2, xlt1),(bx+a^(2),xge1):} is differentiable of all xepsilonR , then

Find the inverse of the function f(x) = In (x^2 + 3x + 1), x in [1, 3] and assuming it to be an onto function.