當(dāng)時(shí).=.當(dāng)且僅當(dāng)x=-y時(shí)取等號(hào). 查看更多

 

題目列表(包括答案和解析)

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f(x,y)為關(guān)于x,y的二元函數(shù),現(xiàn)定義滿足下列性質(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________.

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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f(x,y)為關(guān)于x,y的二元函數(shù).現(xiàn)定義滿足下列性質(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f(x,y)為關(guān)于x,y的二元函數(shù).現(xiàn)定義滿足下列性質(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,()有唯一確定的f(x,y)與之對(duì)應(yīng),則稱f(x,y)為關(guān)于x,y的二元函數(shù).

定義:滿足下列性質(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)2;②f(x,y)=|x-y|;③f(x,y)=

請(qǐng)選出所有能夠成為關(guān)于x,y的廣義“距離”的序號(hào)________

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