Question

（2013•浦東新區(qū)二模）函數(shù)f（x）=1+log₂x與y=g（x）的圖象關(guān)于直線y=x對(duì)稱，則g（3）=

4

．

Answer 1

分析：函數(shù)y=g（x）與函數(shù)f（x）=1+log₂x的圖象關(guān)于直線y=x對(duì)對(duì)稱，說(shuō)明函數(shù)y=g（x）是y=1+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=1+log₂x的反函數(shù)．然后求解函數(shù)值．

解答：解：由y=1+log₂x得，x=2^y-1，所以，函數(shù)y=1+log₂x的反函數(shù)為y=2^x-1，
則函數(shù)y=g（x）的解析式為g（x）=2^x-1．g（3）=2²=4
故答案為：4．

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，此題是基礎(chǔ)題．