已知函数f(x)满足f(x+1/2)=log1/2(x^2-9),

题目

已知函数f(x)满足f(x+1/2)=log1/2(x^2-9),
若函数f(x)的定义域为[-2,-1）时,求其反函数f-1(x) .

答案

令a=x+1/2
x=a-1/2
故f(a)=log1/2[(a-1/2)²-9]=log1/2(a²-a-35/4)
f(x)=log1/2(x²-x-35/4)
因-2≤x