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        1. 當(dāng)且僅當(dāng)x=時(shí).等號(hào)成立. 查看更多

           

          題目列表(包括答案和解析)

          若對(duì)任意x∈A,y∈B,()有唯一確定的f(x,y)與之對(duì)應(yīng),則稱(chēng)f(x,y)為關(guān)于x,y的二元函數(shù).現(xiàn)定義滿(mǎn)足下列性質(zhì)的二元函數(shù)f(x,y)為關(guān)于實(shí)數(shù)x,y的廣義“距離”:

          (1)非負(fù)性:f(x,y)≥0,當(dāng)且僅當(dāng)x=y(tǒng)時(shí)取等號(hào);

          (2)對(duì)稱(chēng)性:f(x,y)=f(y,x);

          (3)三角形不等式:f(x,y)≤f(x,z)+f(z,y)對(duì)任意的實(shí)數(shù)z均成立.

          今給出三個(gè)二元函數(shù),請(qǐng)選出所有能夠成為關(guān)于x,y的廣義“距離”的序號(hào):

          ①f(x,y)=|x-y|;②f(x,y)=(x-y)2;③f(x,y)=

          ________.

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          若對(duì)任意x∈A,y∈B,()有唯一確定的f(x,y)與之對(duì)應(yīng),則稱(chēng)f(x,y)為關(guān)于x,y的二元函數(shù).現(xiàn)定義滿(mǎn)足下列性質(zhì)的二元函數(shù)f(x,y)為關(guān)于實(shí)數(shù)x,y的廣義“距離”:

          (1)非負(fù)性:f(x,y)≥0,當(dāng)且僅當(dāng)x=y(tǒng)時(shí)取等號(hào);

          (2)對(duì)稱(chēng)性:f(x,y)=f(y,x);

          (3)三角形不等式:f(x,y)≤f(x,z)+f(z,y)對(duì)任意的實(shí)數(shù)z均成立.

          今給出三個(gè)二元函數(shù),請(qǐng)選出所有能夠成為關(guān)于x,y的廣義“距離”的序號(hào):

          ①f(x,y)=|x-y);②f(x,y)=f(x-y)2;③

          ________

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          若對(duì)任意x∈A,y∈B(AR,BR)有唯一確定的f(x,y)與之對(duì)應(yīng),則稱(chēng)f(x,y)為關(guān)于x,y的二元函數(shù),現(xiàn)定義滿(mǎn)足下列性質(zhì)的f(x,y)為關(guān)于實(shí)數(shù)x,y的廣義“距離”:

          (1)非負(fù)性:f(x,y)≥0,當(dāng)且僅當(dāng)x=y(tǒng)時(shí)取等號(hào);

          (2)對(duì)稱(chēng)性:f(x,y)=f(y,x);

          (3)三角形不等式:f(x,y)≤f(x,z)+f(z,y)對(duì)任意的實(shí)數(shù)z均成立.給出三個(gè)二元函數(shù):

          ①f(x,y)=|x-y|;

          ②f(x,y)=(x-y)2;

          ③f(x,y)=

          則所有能夠成為關(guān)于x,y的廣義“距離”的序號(hào)為_(kāi)_______.

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          若對(duì)任意的x∈A,y∈B,(A⊆R,B⊆R),有唯一確定的f(x,y)與之對(duì)應(yīng),則稱(chēng)f(x,y)為關(guān)于x、y的二元函數(shù).現(xiàn)定義滿(mǎn)足下列性質(zhì)的二元函數(shù)f(x,y)為關(guān)于實(shí)數(shù)x、y的廣義“距離”:
          (1)非負(fù)性:f(x,y)≥0,當(dāng)且僅當(dāng)x=y時(shí)取等號(hào);
          (2)對(duì)稱(chēng)性:f(x,y)=f(y,x);
          (3)三角形不等式:f(x,y)≤f(x,z)+f(z,y)對(duì)任意的實(shí)數(shù)z均成立.
          今給出下列四個(gè)二元函數(shù):①f(x,y)=|x-y|;、趂(x,y)=(x-y)2
          數(shù)學(xué)公式; ④f(x,y)=x2+y2
          能夠稱(chēng)為關(guān)于實(shí)數(shù)x、y的廣義“距離”的函數(shù)的序號(hào)是________.

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          設(shè)函數(shù)f(x)=ex-x-1,g(x)=e2x-x-7.
          (1)解不等式f(x)≤g(x);
          (2)事實(shí)上:對(duì)于?x∈R,有f(x)≥0成立,當(dāng)且僅當(dāng)x=0時(shí)取等號(hào).由此結(jié)論證明:(1+
          1x
          )x
          <e,(x>0).

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