Consider the function \( f : (0,2) \to \mathbb{R} \) defined by \( f(x)=\frac{x}{2}+\frac{2}{x} \) and the function \( g(x) \) defined by
g is continuous but not differentiable at \( x=1 \)
g is not continuous for all \( x\in(0,2) \)
g is continuous and differentiable for all \( x\in(0,2) \)
g is neither continuous nor differentiable at \( x=1 \)
