函数fx=1/2(a^x+a^-x)(a>0,且a不等于1 若函数图象经过点(2,41/9) 求fx

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函数fx=1/2(a^x+a^-x)(a>0,且a不等于1 若函数图象经过点(2,41/9) 求fx

函数fx=1/2(a^x+a^-x)(a>0,且a不等于1 若函数图象经过点(2,41/9) 求fx
函数fx=1/2(a^x+a^-x)(a>0,且a不等于1 若函数图象经过点(2,41/9) 求fx

函数fx=1/2(a^x+a^-x)(a>0,且a不等于1 若函数图象经过点(2,41/9) 求fx
将点(2,41/9)代入函数,得:
41/9=1/2(a²+a^(-2))
∴a=±3或±1/3
∵a>0
∴a=3或1/3
f(x)=1/2(3^x+1/3^x)

依题意有f(2)=41/9
即:(a²+1/a²)=82/9
(a+1/a)²=a²+1/a²+2=100/9,则a+1/a=10/3 ````````````````````````①
(a-1/a)²=a²+1/a²-2=-64/9,则a-1/a=8/3,或...

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依题意有f(2)=41/9
即:(a²+1/a²)=82/9
(a+1/a)²=a²+1/a²+2=100/9,则a+1/a=10/3 ````````````````````````①
(a-1/a)²=a²+1/a²-2=-64/9,则a-1/a=8/3,或1/a-a=8/3·················②
①+②则a+1/a+a-1/a=2a=6,或2/a=6
即a=3或1/3
f(x)=......

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