已知函数f（x）=4-
（Ⅰ）求证：f（x）在（0，+∞）上是增函数； （Ⅱ）若f（x）在[m，n]上的值域是[m，n]（0＜m＜n），求m、n的值． |
（Ⅰ）证明：设x1，x2∈（0，+∞），且x1＜x2，
则f(x1)-f(x2)=(4-
)-(4-1 x1
)1 x2
=
-1 x2
=1 x1
．x1-x2 x1x2
∵x1，x2∈（0，+∞），且x1＜x2，
∴x1-x2＜0，x1x2＞0，
则f(x1)-f(x2)=
＜0．x1-x2 x1x2
即f（x1）＜f（x2）．
∴f（x）在（0，+∞）上是增函数；
（Ⅱ）∵f（x）在（0，+∞）上是增函数，
又f（x）在[m，n]上的值域是[m，n]（0＜m＜n），
∴
，f(m)=4-
=m1 m f(n)=4-
=n1 n
解得：
．m=2- 3 n=2+ 3
∴m=2-
，n=2+3
．3
阅读短文，根据短文内容完成表格，每空一词。（本题共5分每空1分） Many of us have ever loved the two toy bears—a brown Teddy bear and a yellow Winnie-the-Pooh bear. The two toy bears come from real stories in life. In 1902, Theodore Roosevelt, President of the USA, went on hunting. The hunting dogs found an old bear in the forest near Washington D.C. and the guide asked the president to shoot (射杀) it. But President Roosevelt disagreed. A cartoonist (漫画家) drew a cartoon showing that the president refused to shoot the beat. Soon, the bear began to appear in other newspapers. People named the bear Teddy which was Theodore’s nickname (昵称). In 1913, a captain named Harry Cole bourn paid 20 dollars for a black bear which was born in the Canadian country side. The captain’s hometown, Winnipeg, was the origin (起源) of the bear’s name. In Winnipeg, Winnie served as the mascot (吉祥物). When Would War I began, the captain went to France. Winnie was sent to London Zoo which many kids often visited. Because of its lovely look, the bear became popular with children.
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