已知函数f(x)=log2(x+1)(x-1)求函数的定义域单调区间奇偶性？

Question

如题所述

Answer 1

f(x)=log<2>[(x+1)(x-1)]
(x+1)(x-1)>0
x<-1 or x>1
定义域 = (-∞, -1) U (1, +∞)
f(x)=log<2>[(x+1)(x-1)]
f'(x) = (1/ln2) { (2x )/ [(x+1)(x-1)] }
单调
增加 (1, +∞)
减小 (-∞, -1)
f(x)=log<2>[(x+1)(x-1)]
f(-x)
=log<2>[(-x+1)(-x-1)]
=log<2>[(x-1)(x+1)]
=f(x)
=> f(x) 偶函数