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 $$g(x) = \begin{cases} \min\{f(t)\},\ 0 < t \leq x & \text{and } 0 < x \leq 1 \\ \frac{3}{2} + x, & 1 < x < 2 \end{cases}$$. Then

A

g is continuous but not differentiable at x = 1

B

g is not continuous for all $$x \in (0, 2)$$

C

g is neither continuous nor differentiable at x = 1

D

g is continuous and differentiable for all $$x \in (0, 2)$$