设集合\(P=\{3,{\log }_{3}a\} \)，\(f(x)=a\cos ⁡2x+1+a\sin ⁡2x=a \sqrt{2}\sin ⁡(2x+ \dfrac{π}{4})+1 \)，\(Q=\left\{f\left(xight)ight\} \)若\(P∩Q=\{0\} \)，则\(P∪Q= (\) \()\) --优优班--学霸训练营

设集合\(P=\{3,{\log }_{3}a\} \)，\(f(x)=a\cos ⁡2x+1+a\sin ⁡2x=a \sqrt{2}\sin ⁡(2x+ \dfrac{π}{4})+1 \)，\(Q=\left\{f\left(x\right)\right\} \)若\(P∩Q=\{0\} \)，则\(P∪Q= (\) \()\)

A．\(\left\{f\left(x\right)\right\} \)

B．\(\left\{3,0,1- \sqrt{2}\right\} \)

C．\(\left\{f\left\{x\right\},3\right\} \)

D．\(\left\{1- \sqrt{2},0,1+ \sqrt{2}\right\} \)

【考点】并集及其运算

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难度：易

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