Function `f(x)={(x-1",",x lt 2),(2x-3",", x ge 2):}` is a continuous function

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

Function f(x) {{:(x+1,xlt2),(2x-2,xgt=2):} is a continuous function

Let f(x)={{:(ax-b,","x le 1),(3x,"," 1 lt x lt 2),(bx^2-a,"," x ge 2):} If f is continuous function then (a,b) is equal to

Let f(x)={{:(x^(3)-1",", x lt2),(x^(2)+3"," , x ge 2):} Then

show that f(x) ={{:( (2x-1)",",if , x lt2),( (3x)/2",,if x ge 2):} is continuous

At x =1, the function given by f(x) = {(x,x lt 1),(2x-1,x ge1):} is (a) Continuous (b) Not continuous ( c) Not defined

If the function f(x)={{:(k +x, "for " x lt1),(4x+3, "for " x ge1):} is continuous at x=1 then k=

At x =1, the function given by f(x) = {(sinx,x lt 0),(2x,x ge 0):} is (a) Continuous (b) Not continuous ( c) Not defined