\(.\) 已知函数\(f(x)=a\)\({\,\!}^{x}\)
\((a > 0,a\neq 1)\)的反函数的图象经过点\(\left( \left. \dfrac{ \sqrt{2}}{2}, \dfrac{1}{2} \right. \right)\)
\(.\)若函数\(g(x)\)的定义域为\(R\)，当\(x∈[-2,2]\)时，有\(g(x)=f(x)\)，且函数\(g(x+2)\)为偶函数，则下列结论正确的是\((\) \()\)
A. \(g(π) < g(3) < g( \sqrt{2})\)
B. \(g(π) < g( \sqrt{2}) < g(3)\) C. \(g( \sqrt{2}) < g(3) < g(π)\) D. \(g( \sqrt{2}) < g(π) < g(3)\)
