If `f(x)=sgn(x^(3)-x)` is discontinuous at `x`

If f(x)={[x^(3)+3:x!=0, is discontinuous at

Let f(x)={{:(,|x|-3,x lt 1),(,|x-2|+a,x ge 1):} g(x)={{:(,2-|x|,x lt 1),(,Sgn(x)-b,x ge 1):} If h(x)=f(x)+g(x) is discontinuous at exactly one point, then which of the following are correct?

Let f(x)={{:(-3+|x|",",-ooltxlt1),(a+|2-x|",",1lexltoo):} and g(x)={{:(2-|-x|",",-ooltxlt2),(-b+"sgn(x),",2lexltoo):} where sgn(x) denotes signum function of x. If h(x)=f(x)+g(x) is discontinuous at exactly one point, then which of the following is not possible?

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

f(x) = (x^(2)+x-2)/(x^(2)-3x+2) is discontinuous at x =

Function f(x)=x-|x| is discontinuous at x=0

Function f(x)=(x^(3)-1)/(x^(2)-3x+2) is discontinuous at

The function f(x) = (|3x-4|)/(3x-4) is discontinuous at

Let f(x)=sgn(x) and g(x)=x(x^(2)-5x+6) The function f(g(x)) is discontinuous at