Question

函數(shù)y=f（x）圖象與y=log₂x的圖象關(guān)于直線y=x對(duì)對(duì)稱(chēng)，則f（x）=________．

Answer 1

2^x
分析：函數(shù)y=f（x）圖象與y=log₂x的圖象關(guān)于直線y=x對(duì)對(duì)稱(chēng)，說(shuō)明函數(shù)y=f（x）是y=log₂x的反函數(shù)，化y=log₂x為指數(shù)式得到x，然后把x和y互換可得y=log₂x的反函數(shù)．
解答：由y=log₂x得，x=2^y，所以，函數(shù)y=log₂x的反函數(shù)為y=2^x，
則函數(shù)y=f（x）的解析式為f（x）=2^x．
故答案為2^x．
點(diǎn)評(píng)：本題考查反函數(shù)的求法，考查指數(shù)式和對(duì)數(shù)式的互化，指數(shù)函數(shù)的反函數(shù)是對(duì)數(shù)函數(shù)，對(duì)數(shù)函數(shù)的反函數(shù)是指數(shù)函數(shù)，互為反函數(shù)的兩個(gè)函數(shù)的圖象關(guān)于直線y=x對(duì)稱(chēng)，此題是基礎(chǔ)題．