solve for ,x where `f(x)=|x|ge0`

A single formula that gives f(x) for all x ge0 where f(x)={(3+x, 0lexlt3),(3x-3, xge3):} is

If f (x)= [{:( cos x ^(2),, x lt 0),( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where f (x) =f )|x|) is non-difierentiable.

In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where g (x) =f (|x|) is non-differentiable.

Find lim_(xrarr0) f(x) where f(x)={{:((x)/(|x|),xne0),(0,x=0):}

solve sqrt(x+2) ge x

Let f(x) and g(x) be defined and differntiable for all x ge x_0 and f(x_0)=g(x_0) f(x) ge (x) for x gt x_0 then

A quadratic function f(x) satisfies f(x)ge0 for all real x. If f(2)=0 and f(4)=12, then the value of f(6) is :

Let f (x)= [{:(x+1,,, x lt0),((x-1),,, x ge0):}and g (x)=[{:(x+1,,, x lt 0),((x-1)^(2),,, x ge0):} then the number of points where g (f(x)) is not differentiable.

If f(x) ge0 for all x, then f(2-x) is

Number of points where f (x)= {{:(max(|x ^(2)- x-2|","x ^(2) -3x),,, x ge0),( max (ln (-x)"," e ^(x)),,, x lt 0):} is non-differentiable will be: