Check continuity and differentiability of g(x) = `|x-2| + |x|`

Let f(x)={[x], for -2<=x<=-(1)/(2),2x^(2)-1 for -(1)/(2)<=x<=2 and g(x)=f(|x|)+|f(x)|. Check the continuity and differentiability of g(x) in (-2,2).

Discuss the continuity and differentiability of f(x)={1-x ,\ \ \ \ x 2

Let f(x)=[-1 if -2 <= x <= 0 |x-1| if 0 < x <= 2 and g(x)=int_-2^x f(t) d t. Define g(x) as a function of x and test the continuity and differentiability of g(x) i n (-2,2).

Discuss the continuity and differentiability of 1-x,x 2

Discuss the continuity and differentiability of f(x)={1-x ,x 2

Discuss the continuity and differentiability of f(x)={1-x ,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x 2

F(x)=x^(3)-3x^(2)+6 and g(x)=max{F(t):x+1 =0 Find continuity and differentiability of g(x) for x in[-3,1]

Define continuity and differentiability of a function at a point verify the continuity and differentiability of the function: , f(x)={[(1-x),x 2])

Check the differentiability of f(x)=tan|x|-|x| at x=0