Discuss the continuity of `f(x)=|x|sgn(x^3-x)`

Discuss the continuity of f(x)=sgn(x^3-x)

Discuss the continuity of f(x)=sgn(x^2-2x+3)

Discuss the continuity of f(x)=(log|x|)sgn(x^2-1),x!=0.

Discuss the continuity of f(x)=sgn(2cosx-1)

Discuss the continuity of f(x)={|x|cos(1/x),\ \ \ x!=0 0,\ \ \ \ x=0 at x=0

Discuss continuity of (i) f(x) = sgn(x^(3)-x) (ii) f(x) = sgn(2 cos x-1) (iii) f(x) = sgn(x^(2)-2x+3)

Discuss the continuity of f(x)={(x-a)sin(1/(x-a)),\ \ \ x!=a\ \ \ \ \ \ \ \ \ \ \ \ 0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=a at x=a

Discuss the continuity of f(x)={(x^2)/(|x|),x!=0 0,x=0

Discuss the continuity of f(x)={1/(e^(x-1)),x!=1 0,x=1

Discuss the continuity of f(x) ={:{(sin""(1)/(x)", "x ne 0),(" "1", " x= 0):},