Let $f\left(x\right)$ be a function for all $x\in R \text{and }f\left(0\right)=1\text{. Then }g\left(x\right)=f\left(\right|x\left|\right)-\sqrt{\frac{1-\cos 2x}{2}}\text{, at }x=0\text{,}$

is non- differentiable at $x = 0$ as its graph has vertical tangent at $x = 0$

is differentiable at $x = 0$ and its value is 0

is differentible at $x = 0$ and its value is 1

is non- differentiable at $x = 0$ as its graph has sharp turn at $x = 0$