设函数f（x）=2x,x<0log2x,x>0，若对任意给定的t∈（1，+∞），都存在唯一的x∈R，满足f（f（x））=2at2+at，则正实数a的最小值是

题干

设函数f（x）=2x,x<0log2x,x>0，若对任意给定的t∈（1，+∞），都存在唯一的x∈R，满足f（f（x））=2at²+at，则正实数a的最小值是（　　）

A：1

B： $\frac{1}{2}$

C： $\frac{1}{3}$

D： $\frac{1}{4}$

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C

B

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