y=log1/3 ^2(x ) +log1/3( x)
設(shè)log1/3( x)=t,
則y=t^2+t,
原函數(shù)由函數(shù)y=t^2+t與函數(shù)t =log1/3( x)復(fù)合而成.
函數(shù)t =log1/3( x)在定義域上是單調(diào)遞減的,
根據(jù)復(fù)合函數(shù)“同增異減”的原則,
所以求原函數(shù)的單調(diào)遞減區(qū)間就是求函數(shù)y=t^2+t的遞增區(qū)間.
y=t^2+t=(t+1/2)^2-1/4,
當(dāng)t≥-1/2時(shí)該函數(shù)單調(diào)遞增,
即log1/3( x) ≥-1/2
所以0