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

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

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

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

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

Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|),x!=1,2, 6,x=1, 12 ,x=2

Discuss the continuity of f(x)= {x^2, x is rational -x^2,x is irrational

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

Draw the graph and discuss the continuity of f (x) = [sin x + cos x], x in [0, 2pi), where [.] represents the greatest integer function.

Let f(x)={(1+3x)^(1/x), x != 0e^3,x=0 Discuss the continuity of f(x) at (a) x=0, (b) x=1

If f(x)={x-2, x le 0 and 4-x^2,x > 0, then discuss the continuity of y=f(f(x)).