A function is defined as follows `f (x) ={x^3,x^2 lt 1 and x , x^2 leq 1` then function is

A function is defined as follows f(x)={x^(3),x^(2)<1 and x,x^(2)<=1 then function is

A function is defined as follows f(x)={:{(x^(3),, x^(2)lt1),(x, , x^(2)ge 1):} then function is

A function is defined as follows f(x)={:{(x^(3),, x^(2)lt1),(x, , x^(2)ge 1):} then function is

A function f is defined as follows : f(x) = {{:(0," for ",x lt 0),(x ," for ",0 le x lt 1),(-x^(2)+4x-2," for ",1lexlt3),(4-x ," for ",xge3):} Is the function continuous ?

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 in a lt x lt b and a lt x_(1) lt x_(2) lt b , then f(x) is strictly monotonic decreasing in a le x le b when-

Prove that the function f defined by f(x) = x^3 + x^2 -1 is a continuous function at x= 1.