函數(shù)g(x)=logax+x-4的零點(diǎn)是函數(shù)y=logax與函數(shù)y=4-x圖象交點(diǎn)B的橫坐標(biāo),
由于指數(shù)函數(shù)與對(duì)數(shù)函數(shù)互為反函數(shù),
其圖象關(guān)于直線y=x對(duì)稱,
直線y=4-x與直線y=x垂直,
故直線y=4-x與直線y=x的交點(diǎn)(2,2)即是A,B的中點(diǎn),
∴m+n=4,
∴
1 |
m |
1 |
n |
1 |
4 |
1 |
m |
1 |
n |
1 |
4 |
m |
n |
n |
m |
當(dāng)m=n=2等號(hào)成立,
而m+n=4,故
1 |
m |
1 |
n |
故所求的取值范圍是[1,+∞).
故選B.