已知fx为偶函数，在[0，+∞）上为增函数，若f（log以2为底x）＞f（1）,则x的取值范围为 已知偶函数f（x）在[0，+∞）上为增函数，且f（ ...
\u5df2\u77e5f\uff08x\uff09\u4e3a\u5076\u51fd\u6570\uff0c\u5728[0\uff0c+\u221e\uff09\u4e0a\u4e3a\u589e\u51fd\u6570\uff0c\u82e5f\uff08log2x\uff09\uff1ef\uff081\uff09\uff0c\u5219x\u7684\u53d6\u503c\u8303\u56f4\u4e3a\uff08\u3000\u3000\uff09A\uff0e\uff082\uff0c+\u2235f\uff08x\uff09\u4e3a\u5076\u51fd\u6570\uff0c\u5728[0\uff0c+\u221e\uff09\u4e0a\u4e3a\u589e\u51fd\u6570\u2234f\uff08x\uff09\u5728\uff08-\u221e\uff0c0\uff09\u4e0a\u4e3a\u51cf\u51fd\u6570\u2234f\uff08log2x\uff09\uff1ef\uff081\uff09?|log2x|\uff1e1\uff0c\u5373log2x\uff1e1\u6216log2x\uff1c-1\u53730\uff1cx\uff1c12\u6216x\uff1e2\u6545\u9009B
\u56e0\u4e3af\uff08 1 2 \uff09=0\uff0e\u6240\u4ee5\u4e0d\u7b49\u5f0ff\uff08log a x\uff09\uff1e0 \u7b49\u4ef7\u4e8ef\uff08log a x\uff09\uff1ef\uff08 1 2 \uff09\u56e0\u4e3a\u5076\u51fd\u6570f\uff08x\uff09\u5728[0\uff0c+\u221e\uff09\u4e0a\u662f\u589e\u51fd\u6570\uff0c\u6240\u4ee5\uff08-\u221e\uff0c0\uff09\u4e0a\u662f\u51cf\u51fd\u6570\uff081\uff09\u5f53log a x\u22650\u65f6\uff0clog a x\uff1e 1 2 \u82e50\uff1ca\uff1c1\uff0c\u89e3\u5f970\uff1cx\uff1c a \uff1b\u82e5a\uff1e1\uff0c\u89e3\u5f97x\uff1e a \uff1b\uff082\uff09\u5f53log a x\uff1c0\u65f6\uff0clog a x\uff1c- 1 2 \uff1b\u82e50\uff1ca\uff1c1\uff0c\u89e3\u5f97x\uff1e a a \uff1b\u82e5a\uff1e1\uff0c\u89e3\u5f970\uff1cx\uff1c a a \uff1b\u5373\uff1a0\uff1ca\uff1c1\u65f6\u4e0d\u7b49\u7684\u89e3\u96c6\uff080\uff0c a \uff09\u222a\uff08 a a \uff0c+\u221e\uff09\uff1ba\uff1e1\u65f6\u4e0d\u7b49\u7684\u89e3\u96c6\uff080\uff0c a a \uff09\u222a\uff08 a \uff0c+\u221e\uff09\uff1b
因为f（x）是偶函数，且f（1/2)=0所以f（-1/2）=f（1/2）=0因为f（x）在【0，+∞) 上为增函数所以f（x）在（-∞，-1/2）∪（1/2，+∞）上＞0所以log1/4 x＜-1/2或log1/4 x＞1/2∴x＞2或0＜x＜1/2Ilog2（x）I＞1=log2(2)
∴0∠x＜1/2或x＞2
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