¸ø³öÏÂÁÐËĸöÃüÌ⣺
¢ÙÈç¹ûÃüÌâ¡°?p¡±ÓëÃüÌâ¡°p»òq¡±¶¼ÊÇÕæÃüÌ⣬ÄÇôÃüÌâqÒ»¶¨ÊÇÕæÃüÌ⣻
¢ÚÒÑÖªÏòÁ¿
a
£¬
b
Âú×ã|
a
|=1£¬|
b
|=4
£¬ÇÒ
a
b
=2
£¬Ôò
a
Óë
b
µÄ¼Ð½ÇΪ
¦Ð
6
£»
¢ÛÈôº¯Êýf£¨x+1£©ÊÇÆ溯Êý£¬f£¨x-1£©ÊÇżº¯Êý£¬ÇÒf£¨0£©=2£¬Ôòf£¨2012£©=2£»
¢ÜÒÑÖªº¯Êýf(x)=log4(4x+1)+kx(k¡ÊR)ÊÇżº¯Êý£¬º¯Êýg(x)=log4(a•2x-
4
3
a)
£¬Èôº¯Êýf£¨x£©µÄͼÏóÓ뺯Êýg£¨x£©µÄͼÏóÓÐÇÒÖ»ÓÐÒ»¸ö¹«¹²µã£¬ÔòʵÊýaµÄÈ¡Öµ·¶Î§ÊÇ£¨1£¬+¡Þ£©£®
ÆäÖÐÕýÈ·ÃüÌâµÄÐòºÅΪ
¢Ù
¢Ù
£®
·ÖÎö£º¸ù¾Ý¸´ºÏÃüÌâÕæ¼ÙÐÔµÄÕæÖµ±í£¬¿ÉÅжϳöÃüÌâ¡°p¡±Îª¼ÙÃüÌ⣬½ø¶øÃüÌâ¡°q¡±ÊÇÕæÃüÌ⣬¿ÉÅжϣ¨1£©£»
¸ù¾ÝÏòÁ¿¼Ð½Ç¹«Ê½£¬½áºÏÒÑÖªÇó³öÁ½¸öÏòÁ¿µÄ¼Ð½Ç£¬¿ÉÅжϣ¨2£©£»
¸ù¾ÝÒÑÖª£¬½áºÏº¯ÊýÆæżÐԵĶ¨Ò壬·ÖÎö³öº¯ÊýµÄÖÜÆÚÐÔ£¬½ø¶øÇó³öf£¨2012£©µÄÖµ£¬¿ÉÅжϣ¨3£©£»
¸ù¾Ýº¯ÊýÆæżÐԵĶ¨Ò壬Çó³ökÖµ£¬½ø¶ø¸ù¾Ýº¯Êýf£¨x£©µÄͼÏóÓ뺯Êýg£¨x£©µÄͼÏóÓÐÇÒÖ»ÓÐÒ»¸ö¹«¹²µã£¬Çó³öʵÊýaµÄÈ¡Öµ·¶Î§£¬¿ÉÅжϣ¨4£©£®
½â´ð£º½â£ºÈôÃüÌâ¡°?p¡±ÓëÃüÌâ¡°p»òq¡±¶¼ÊÇÕæÃüÌ⣬ÔòÃüÌâ¡°p¡±Îª¼ÙÃüÌ⣬ÃüÌâ¡°q¡±ÊÇÕæÃüÌ⣬¹Ê¢ÙÕýÈ·£»
Èô|
a
|=1£¬|
b
|=4
£¬ÇÒ
a
b
=2
£¬Ôò
a
Óë
b
µÄ¼Ð½Ç¦ÈÂú×㣬cos¦È=
a
b
|
a
|•|
b
|
=
1
2
£¬Ôò
a
Óë
b
µÄ¼Ð½ÇΪ
¦Ð
3
£¬¹Ê¢Ú´íÎó£»
Èôº¯Êýf£¨x+1£©ÊÇÆ溯Êý£¬f£¨x+1£©=-f£¨-x+1£©£¬Èôf£¨x-1£©ÊÇżº¯Êý£¬Ôòf£¨x-1£©=f£¨-x-1£©
¹Êf£¨x+4£©=f£¨x+3+1£©=-f[-£¨x+3£©+1]=-f£¨-x-2£©=-f[-£¨x+1£©-1]=-f£¨x+1-1£©=-f£¨x£©
Ôòf£¨x+8£©=-f£¨x+4£©=f£¨x£©£¬¼´º¯Êýf£¨x£©µÄÖÜÆÚΪ8£¬ÓÉf£¨0£©=2£¬Ôòf£¨2012£©=f£¨4£©=-2£¬¹Ê¢Û´íÎó£»
ÓÉf£¨x£©ÎªÅ¼º¯Êý£¬¹Êlog4£¨4-x+1£©-kx=log4£¨4x+1£©+kx¶ÔËùÓÐx¡ÊR¶¼³ÉÁ¢£¬¼´£¨2k+1£©x=0¶ÔËùÓÐx¡ÊR¶¼³ÉÁ¢£¬¹Êk=-
1
2
£®
ÓÉ·½³Ìlog4£¨4x+1£©-
1
2
x=log4(a•2x-
4
3
a)
£¨*£©
¿É±äÐÎΪ
4x+1
2x
=a•2x-
4
3
a£¬¢Ù
a•2x-
4
3
a£¾0£¬¢Ú
£¬ÓÉ¢ÚµÃ
a£¾0
2x£¾
4
3
»ò
a£¼0
2x£¼
4
3
£¬
Áî2x=t£¬Ôò
a£¾0
t£¾
4
3
£¬»ò
a£¼0
0£¼t£¼
4
3

Óɢٵã¨a-1£©£¨2x£©2-
4
3
a•2x-1=0£¬Éèh£¨t£©=£¨a-1£©t2-
4
3
at-1
¡àµ±a£¾0ʱ£¬£¨a-1£©h£¨
4
3
£©£¼0⇒a£¾1£¬
µ±a£¼0ʱ£¬h£¨0£©=-1£¼0£¬h£¨
4
3
£©£¾0⇒a²»´æÔÚ£¬
µ±¡÷=£¨-
4
3
a£©2+4£¨a-1£©=0ʱ£¬a=
3
4
»òa=-3£¬
Èôa=
3
4
£¬Ôòt=-2£¬²»ºÏÌâÒ⣬ÉáÈ¥£¬Èôa=-3£¬Ôòt=
1
2
£¬Âú×ãÌâÒ⣬
¡àµ±a=-3»òa£¾1ʱ£¬º¯Êýf£¨x£©Óëg£¨x£©µÄͼÏóÓÐÇÒÖ»ÓÐÒ»¸ö¹«¹²µã£¬¹Ê¢Ü´íÎó
¹Ê´ð°¸Îª£º¢Ù
µãÆÀ£º±¾ÌâÒÔÃüÌâµÄÕæ¼ÙÅжÏΪÔØÌ忼²éÁ˺¯ÊýµÄÆæżÐÔÓëÖÜÆÚÐÔ£¬¸´ºÏÃüÌ⣬ÏòÁ¿¼Ð½Ç¹«Ê½µÈ֪ʶµã£¬ÆäÖУ¨3£©£¨4£©ÊǺ¯ÊýͼÏóºÍÐÔÖʵÄ×ÛºÏÓ¦Óã¬ÄѶȷdz£´ó£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

12¡¢ÒÑÖªa¡¢bÊÇÁ½Ìõ²»ÖغϵÄÖ±Ïߣ¬¦Á¡¢¦Â¡¢¦ÃÊÇÈý¸öÁ½Á½²»ÖغϵÄƽÃ棬¸ø³öÏÂÁÐËĸöÃüÌ⣺
¢ÙÈôa¡Í¦Á£¬a¡Í¦Â£¬Ôò¦Á¡Î¦Â£»
¢ÚÈô¦Á¡Í¦Ã£¬¦Â¡Í¦Ã£¬Ôò¦Á¡Î¦Â£»
¢ÛÈô¦Á¡Î¦Â£¬a?¦Á£¬b?¦Â£¬Ôòa¡Îb£»
¢ÜÈô¦Á¡Î¦Â£¬¦Á¡É¦Ã=a£¬¦Â¡É¦Ã=b£¬Ôòa¡Îb£®
ÆäÖÐÕýÈ·ÃüÌâµÄÐòºÅÓÐ
¢Ù¢Ü
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¸ø³öÏÂÁÐËĸöÃüÌ⣺
¢Ùº¯Êýy=
1
x
µÄµ¥µ÷¼õÇø¼äÊÇ£¨-¡Þ£¬0£©¡È£¨0£¬+¡Þ£©£»
¢Úº¯Êýy=x2-4x+6£¬µ±x¡Ê[1£¬4]ʱ£¬º¯ÊýµÄÖµÓòΪ[3£¬6]£»
¢Ûº¯Êýy=3£¨x-1£©2µÄͼÏó¿ÉÓÉy=3x2µÄͼÏóÏòÓÒƽÒÆ1¸öµ¥Î»µÃµ½£»
¢ÜÈôº¯Êýf£¨x£©µÄ¶¨ÒåÓòΪ[0£¬2]£¬Ôòº¯Êýf£¨2x£©µÄ¶¨ÒåÓòΪ[0£¬1]£»
¢ÝÈôA={s|s=x2+1}£¬B={y|x=
y-1
}
£¬ÔòA¡ÉB=A£®
ÆäÖÐÕýÈ·ÃüÌâµÄÐòºÅÊÇ
¢Û¢Ü¢Ý
¢Û¢Ü¢Ý
£®£¨ÌîÉÏËùÓÐÕýÈ·ÃüÌâµÄÐòºÅ£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

½«±ß³¤Îª2£¬Èñ½ÇΪ60¡ãµÄÁâÐÎABCDÑؽ϶̶ԽÇÏßBDÕ۳ɶþÃæ½ÇA-BD-C£¬µãE£¬F·Ö±ðΪAC£¬BDµÄÖе㣬¸ø³öÏÂÁÐËĸöÃüÌ⣺
¢ÙEF¡ÎAB£»¢ÚÖ±ÏßEFÊÇÒìÃæÖ±ÏßACÓëBDµÄ¹«´¹Ïߣ»¢Ûµ±¶þÃæ½ÇA-BD-CÊÇÖ±¶þÃæ½Çʱ£¬ACÓëBD¼äµÄ¾àÀëΪ
6
2
£»¢ÜAC´¹Ö±ÓÚ½ØÃæBDE£®
ÆäÖÐÕýÈ·µÄÊÇ
¢Ú¢Û¢Ü
¢Ú¢Û¢Ü
£¨½«ÕýÈ·ÃüÌâµÄÐòºÅÈ«ÌîÉÏ£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¸ø³öÏÂÁÐËĸöÃüÌ⣬ÆäÖÐÕýÈ·µÄÃüÌâµÄ¸öÊýΪ£¨¡¡¡¡£©
¢ÙÃüÌâ¡°?x0¡ÊR£¬2x0¡Ü0¡±µÄ·ñ¶¨ÊÇ¡°?x¡ÊR£¬2x£¾0¡±£»
¢Úlog2sin
¦Ð
12
+log2cos
¦Ð
12
=-2£»
¢Ûº¯Êýy=tan
x
2
µÄ¶Ô³ÆÖÐÐÄΪ£¨k¦Ð£¬0£©£¬k¡ÊZ£»
¢Ü[cos£¨3-2x£©]¡ä=-2sin£¨3-2x£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¸ø³öÏÂÁÐËĸöÃüÌ⣺
¢Ùº¯Êýy=ax£¨a£¾0ÇÒa¡Ù1£©Ó뺯Êýy=logaax£¨a£¾0ÇÒa¡Ù1£©µÄ¶¨ÒåÓòÏàͬ£»
¢Úº¯Êýy=x3Óëy=3xµÄÖµÓòÏàͬ£»
¢Ûº¯Êýy=
1
2
+
1
2x-1
Óëy=
(1+2x)2
x•2x
¶¼ÊÇÆ溯Êý£»
¢Üº¯Êýy=£¨x-1£©2Óëy=2x-1ÔÚÇø¼ä[0£¬+¡Þ£©É϶¼ÊÇÔöº¯Êý£¬ÆäÖÐÕýÈ·ÃüÌâµÄÐòºÅÊÇ£¨¡¡¡¡£©

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸