已知ab属于R,且a不等于b,试求函数f(x)=[a^2x+(ab)^x-2b^2x]^(-1\2)的定义域

a,b∈R,a≠b,函数f(x) = [a2x + (ab)x – 2b2x]-1/2 = 1/√[a2x + (ab)x – 2b2x] => a2x + (ab)x – 2b2x > 0 => (ax - bx)(ax + 2bx) > 0,由题意,a > 0且a≠1,b > 0且b≠1,a≠b,故ax > 0,bx > 0 => ax + 2bx > 0 => ax - bx > 0 => ax > bx => (a/b)x > 1 = (a/b)0,分类讨论：
1）当a > b > 0时,a/b > 1 => 函数的定义域为x > 0；
2）当b > a > 0时,a/b < 1 => 函数的定义域为x < 0.