Consider the function $\mathrm{f}:(0,2) \rightarrow \mathrm{R}$ defined by $f(x)=\frac{x}{2}+\frac{2}{x}$ and the function $g(x)$ defined by $g(x)= \left\{\begin{array}{cc}\min \{f(t)\}, & 0
Select the correct option:
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 $x \in(0,2)$
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