Question

y=log2x-1分之x〔x＞1〕的反函数解题步骤

Answer 1

y=log2x-1分之x〔x＞1〕的反函数

由y为以2为底,x-1分之x即x/(x-1)的对数,

得2^y=x/(x-1)

2^y(x-1)=x

x*(2^y)-2^y=x

x*(2^y)-x=2^y

x(2^y-1)=2^y

x=2^y/(2^y-1)

即

y=2^x/(2^x-1) (x≠0)

∴y=log2x-1分之x〔x＞1〕的反函数是:

y=2^x/(2^x-1) (x≠0).

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