函數(shù)y=2x+1(x∈R)的反函數(shù)是________.
y=log2x-1
分析:欲求原函數(shù)的反函數(shù),即從原函數(shù)式y(tǒng)=2x+1(x∈R)中反解出x,后再進行x,y互換,即得反函數(shù)的解析式.
解答:由y=2x+1得 x+1=log2y,
即x=-1+log2y,
又∵原函數(shù)的值域是y>0,
∴函數(shù)y=2x+1(x∈R)的反函數(shù)是y=-1+log2x(x>0).
故答案為y=-1+log2x.
點評:本題考查反函數(shù)的求法,屬于基礎題目,要會求一些簡單函數(shù)的反函數(shù),掌握互為反函數(shù)的函數(shù)圖象間的關系.求反函數(shù),一般應分以下步驟:(1)由已知解析式y(tǒng)=f(x)反求出x=Ф(y);(2)交換x=Ф(y)中x、y的位置;(3)求出反函數(shù)的定義域(一般可通過求原函數(shù)的值域的方法求反函數(shù)的定義域).