已知f（x）是定义在（0，+∞）上的增函数，且f(
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∵f(
)=f(x)-f(y)，f（3）=1．，x y
∴f（
）=f（9）-f（3）=1，f（9）=f（3）+f（3）=2，9 3
f（x+5）＜2=f（9），再由f（x）的定义域为（0，+∞），
且在其上为增函数知0＜x+5＜9 解得-5＜x＜4
所以不等式f（x+5）＜2的解集为 {x|-5＜x＜4}．
故答案为：{x|-5＜x＜4}．
The summer vacation is the best time for students. They can go outdoors and have fun. They can go to big cities to , or go to the countryside to enjoy the beauty of . Peter is an American middle school student and he loves very much. He always travels in his country. This summer vacation he wants to do . He is interested in Chinese history. he is flying to Beijing and Xi’an for the summer vacation. He is leaving on July 12th and New York on the last day of the month. He plans a fantastic vacation. During the , he is visiting places of interest and going shopping. At night, he is to enjoy the night views. He is sure he will have a time.
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