定义域有不等式组
(x+1)/(x-1) >0........(1)
x-1>0 ...........(2)
p-x>0 ..........(3)
====>定义域1<x<p
f(x)
=log(2) [(x+1)/(x-1)]+log(2)(x-1)+log(2)(p-x)
=log(2)[(x+1)(p-x)]
真数可化为
t=g(x)=-[x - (p-1)/2]² +(p+1)²/4
p>1 ===>p>(p-1)/2
讨论:
当,1<(p-1)/2 <p ===>p>3
==>值域
f(x)<log(2)(p+1)²/4 =2log(2)(p+1) -2
当(p-1)/2≤1 ===>1<p≤3
-[x - (p-1)/2]² +(p+1)²/4无最大最小但是t<g(1)
==>t<2(p-1)
==>值域
f(x)<1+log(2)(p-1)
