Is the function `f(x) = {x} x >= 0 {-x} x < 0` (where {*} denotes the fractional part of (x) even ?

The function f(x) = x |x| at x= 0 is

The function f(x) =|x| at x=0 is

Discuss the continuity of the function f(x) = {:{(x^2, x le 0),(1-x,x>0):} at x = 0

For what value of k is the function f(x) = { k|x|/x, x =0 continuous at x = 0 ?

Discuss the continuity of the function f(x) = {:{(x , if x > 0),(x^2, if x le0):} .

Discuss the continuity of the function f(x)={x ,\ \ \ x >0 ,\ \ \ 1, x=0 ,-x ,\ \ \ x<0 at the point x=0 .

Prove that the function f(x) = {:{((sinx)/x , x < 0),(x^2 +1, x ge0):} is continuous.