怎么求y=2^x/(2^x+1) 的反函數(shù)

數(shù)學(xué)人氣：936 ℃時(shí)間：2020-05-07 22:58:46

優(yōu)質(zhì)解答

反函數(shù)的定義是把原函數(shù)的x當(dāng)做反函數(shù)的y,把原函數(shù)的y當(dāng)作反函數(shù)的x 所以根據(jù)這個(gè)就很容易求出該函數(shù)的反函數(shù)
即x=2^y/(2^y+1),由于這個(gè)可能比較難算,可把2^y當(dāng)作一個(gè)整體再經(jīng)過(guò)計(jì)算得2^y=x/(x-1),可把這個(gè)化為對(duì)數(shù)函數(shù)就是y=log2[x/(x-1)]就是以2為底x/(x-1)的對(duì)數(shù)
所以該函數(shù)的反函數(shù)就是y=log2[x/(x-1)]