高一对数函数2
1个回答

y=(loga(a^2)+loga(x))*(loga (a)+loga (x))

=(2+loga(x))*(1+loga(x))

= (loga(x))^2+3loga(x)+2

令t=loga(x)

则y=t^2+3t+2=(t+3/2)² -1/4,为t的二次函数,

t=-3/2时,y=-1/4.

t=-1或-2时,y=0.

画出y--t图象,图象开口向上,当-1/4≤y≤0时,-2≤t≤-1

所以当值域是[-1/4,0]时,定义域是[-2,-3/2],或[-3/2,-1],或[-2,-1].

下面分情况讨论：

1．a>1时,X∈[2,4],则t= loga(x)∈[loga(2),loga(4)]

①[loga(2),loga(4)]= [-2,-3/2],此时无解.

②[loga(2),loga(4)]= [-3/2,-1],此时无解.

③[loga(2),loga(4)] =[-2,-1],此时无解.

2.0

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