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#1
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ÇÔ¸Õá¡é¤ÓµÍºáººá¹è¹Í¹
ã¤ÃÁÕÇÔ¸Õá¡é¤ÓµÍºáººá¹è¹Í¹¢Í§¢é͹Õé ªèÇ´éǤÃѺ µÍ¹¹Õé¼Áä´é¤ÓµÍº¨Ò¡¡ÒÃà´ÒÍÂèÒ§à´ÕÂÇàÅÂ
¡Ó˹´ãËé $x$ à»ç¹à«µ¢Í§¨Ó¹Ç¹¨ÃÔ§ $f: R \rightarrow R, g: R \rightarrow R$ ·Õè $f^{-1} (x) = log_{3a} (\frac{x}{b})$ áÅÐ $g(x) = -(2a+1)x + (b+2)$ ÊÓËÃѺºÒ§¨Ó¹Ç¹àµçÁ $a,b$ ¶éÒ $g(f(0)) = -16 = (f^{-1} + g)(3)$ áÅéÇ ¨§ËÒ¤èҢͧ $a^b$ (â¤ÇµÒ Áª. 56) µÍº 27 ¢Íº¤Ø³¤ÃѺ
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á¢è§¤³ÔµÏ ¤Ô´ä´é §èÒ´ÒÂàËÅ×Í á¢è§·Ø¡àÁ×èÍ Ãé͹áç á¨é§»ÃШѡÉì ÃѺÃÒ§ÇÑÅ ËÅÒ¡ËÅÒ ÁÒ¡ÁÒ¹ѡ áµèá¢è§ÃÑ¡ ÂÒ¡á·é á¾éã¨à¸Í |
#2
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á·¹ $x=b$ ã¹Êٵâͧ $f^{-1}(x)$ ¨Ðä´éÊÁ¡Òèҡ $g(f(0))=-16$
ÊèǹÊÁ¡Ò÷ÕèÊͧ¡çá·¹¤èÒ仵ÒÁÊÁ¡Òà $(f^{-1}+g)(3)=-16$ ·ÕèàËÅ×Í¡çá¡éËÒ $a,b$ ¤ÃѺ
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site:mathcenter.net ¤Ó¤é¹ |
#3
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¼Á·ÓÁÒáÅéǤÃѺ à¾Õ§áµèäÁèÃÙé¨Ðá¡éÊÁ¡ÒÃã¹áºº·ÕèÁÕ log ´éÇÂÂѧä§
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á¢è§¤³ÔµÏ ¤Ô´ä´é §èÒ´ÒÂàËÅ×Í á¢è§·Ø¡àÁ×èÍ Ãé͹áç á¨é§»ÃШѡÉì ÃѺÃÒ§ÇÑÅ ËÅÒ¡ËÅÒ ÁÒ¡ÁÒ¹ѡ áµèá¢è§ÃÑ¡ ÂÒ¡á·é á¾éã¨à¸Í |
#4
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$f(x)=(3a)^x(b)$ ; $ f(0)=b$
$g(b)=-(2a+1)b + (b+2)=-2ab+2=-16$ $\therefore ab=9...(1)$ $f^{-1}(3)+g(3)$ $=log_{3a}(\frac{3}{b} )+[-(2a+1)3 + (b+2)]$ $=log_{3a}(\frac{3}{b} )-6a+b-1=-16$ $log_{3a}(\frac{3}{b} )=6a-b-15...(2)$ ¨Ò¡ (1) ; $log_{3a}(\frac{3}{b} )=log_{3a}(\frac{3a}{9} )=1-log_{3a}(9 )$ ᷹ŧ㹠(2) ; $1-log_{3a}(9 )=6a-b-15$ $log_{3a}(9 )=b-6a+16$ $9=(3a)^{b-6a+16}=3^{b-6a+16}a^{b-6a+16}$ á·¹ a=3; $3^2=3^{2(b-2)}$ $\therefore b=3$ ¨Ðä´éÇèÒ $a^b=3^3=27$ |
#5
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ÍéÒ§ÍÔ§:
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á¢è§¤³ÔµÏ ¤Ô´ä´é §èÒ´ÒÂàËÅ×Í á¢è§·Ø¡àÁ×èÍ Ãé͹áç á¨é§»ÃШѡÉì ÃѺÃÒ§ÇÑÅ ËÅÒ¡ËÅÒ ÁÒ¡ÁÒ¹ѡ áµèá¢è§ÃÑ¡ ÂÒ¡á·é á¾éã¨à¸Í |
#6
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µÃ§¹Õé¼ÁäÁèÃÙéÇèÒ ËÒÇÔ¸Õ¤Ô´ÍÂèÒ§äà à¾ÃÒÐÁÕ1 ÊÁ¡Òà áµè 2µÑÇá»Ã
à¹Í¡¨Ò¡¡ÒÃá·¹¤èÒ µÍ¹áá á·¹ a=1 ¡è͹ áµèÂѧäÁèãªè àÅÂá·¹ a=3 ä´é¤ÓµÍº |
#7
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#3
ºÍ¡ÇèÒ·ÓÁÒáÅéÇáµèµÔ´ ÍÂÒ¡·ÃÒºÇèÒ·Ó¶Ö§ä˹áÅéÇ |
#8
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¼Á·Ó¶Ö§ $9=3^{b-6a+16}a^{b-6a+16}$ àËÁ×͹¤Ø³ ln¾wsкØñsÊØñxÅèo ÍèФÃѺ
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á¢è§¤³ÔµÏ ¤Ô´ä´é §èÒ´ÒÂàËÅ×Í á¢è§·Ø¡àÁ×èÍ Ãé͹áç á¨é§»ÃШѡÉì ÃѺÃÒ§ÇÑÅ ËÅÒ¡ËÅÒ ÁÒ¡ÁÒ¹ѡ áµèá¢è§ÃÑ¡ ÂÒ¡á·é á¾éã¨à¸Í |
#9
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a,b à»ç¹¨Ó¹Ç¹àµçÁ ´Ñ§¹Ñ鹨ÐÁÕ $(a,b)$ 3 ¤Ùè ¡çá·¹ä´éàŤÃѺ
(a>0)
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#10
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#8
·ÓãËéàËÅ×͵ÑÇá»Ãà´ÕÂÇ¡è͹´ÕäËÁ¤ÃѺ edit ¨Ñ´ÃÙ»µèÍÍÕ¡¹Ô´¡è͹ 26 ¡ØÁÀҾѹ¸ì 2013 13:24 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Amankris |
#11
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¢Íº¤Ø³·Ø¡¤¹ÁÒ¡¤ÃѺ ^^
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á¢è§¤³ÔµÏ ¤Ô´ä´é §èÒ´ÒÂàËÅ×Í á¢è§·Ø¡àÁ×èÍ Ãé͹áç á¨é§»ÃШѡÉì ÃѺÃÒ§ÇÑÅ ËÅÒ¡ËÅÒ ÁÒ¡ÁÒ¹ѡ áµèá¢è§ÃÑ¡ ÂÒ¡á·é á¾éã¨à¸Í |
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