Question

已知方程|x|=ax+1有一個(gè)負(fù)根而沒(méi)有正根,則實(shí)數(shù)a的取值范圍是____________.

Answer 1

a≥1

解析:令f(x)=|x|,g(x)=ax+1,如圖,函數(shù)y=|x|的圖象記為:l₁:y=x(x≥0);l₂:y=x(x＜0),函數(shù)g(x)=ax+1的斜率為a且過(guò)點(diǎn)(0,1)的直線(xiàn)記為l,根據(jù)題意知,l與l₂有交點(diǎn),而與l₁無(wú)交點(diǎn),由此可得a≥1.