Discuss the continuity of the function `f(x)={{:((e^(1/(x-1))-2)/(e^(1/(x-1))+2)" , "x !=1 ),( 1 " , " x=1):}`

Discuss the continuity of the function f(x)=x^3+x^2-1

Discuss the continuity of the function f(x) = |x -1| at x=1

Examine the continuity of the function f(x) = {((e^((1)/(x)))/(1 + e^((1)/(x)))",","if " x ne 0),(0",","if" x = 0):} at x= 0

Discuss the continuity of the function f defined by f(x) = 1/(x-1) , x ne 1

Discuss the continuity of the function : f(x)={{:(x", "0lexlt1/2),(1/2", "x=1/2),(1-x", "1/2ltxle1):} at x=1/2

Discuss the continuity of the function f(x)=|x-1|+|x-2| at x=1 and x=2

Discuss the continuity of the function : f(x)={{:((1-cosx)/x^(2)", "xne0),(1", "x=0):} at x = 0.