The function defined by `f(x)={x^3-1 ; 1 lt x oo and x-1 ; -oo lt x leq 1` is

A function defined by f(x)=x+a for x lt 0; x for 0 leq x lt 1; b-x for x geq 1 is continuous in [-2,2]. Show that (a+b) is even

At the point x = 1 , then function f(x) = {{:(x^(3) - 1, 1lt x lt oo),(x - 1 , 1 - oolt x le 1):} is

At the point x = 1 , then function f(x) = {{:(x^(3) - 1, 1lt x lt oo),(x - 1 , 1 - oolt x le 1):} is

If function defined by f(x) ={(x-m)/(|x-m|) , x leq 0 and 2x^2+3ax+b , 0 lt x lt 1 and m^2x+b-2 , x leq 1 , is continuous and differentiable everywhere ,

The function f: A->B defined by f(x)=-x^2+6x-8 is a bijection, if A=(-oo,\ 3] and B=(-oo,\ 1] (b) A=[-3,\ oo) and B=(-oo,\ 1] (c) A=(-oo,\ 3] and B=[1,\ oo) (d) A=[3,\ oo) and B=[1,\ oo)

The function f: A->B defined by f(x)=-x^2+6x-8 is a bijection, if A=(-oo,\ 3] and B=(-oo,\ 1] (b) A=[-3,\ oo) and B=(-oo,\ 1] (c) A=(-oo,\ 3] and B=[1,\ oo) (d) A=[3,\ oo) and B=[1,\ oo)

Let a , b in R,(a in 0) . If the funtion f defined as f(x)={{:(,(2x^(2))/(a),0 le x lt 1),(,a,1 le x lt sqrt2),(,(2b^(2)-4b)/(x^(3)),sqrt2lt x lt oo):} is a continous in [0,oo) . Then, (a,b)=