這里是令g(x)=(a^2-1)x^2+(a-1)x+2/(a+1)
則 f(x)=√g(x)
當(dāng)a²-1＞0時(shí) 確保g(x)=(a^2-1)x^2+(a-1)x+2/(a+1)表示一個(gè)開(kāi)口向上的拋物線
△ ≤0 時(shí),確保方程(a^2-1)x^2+(a-1)x+2/(a+1）=0有兩個(gè)相等實(shí)數(shù)根或無(wú)實(shí)數(shù)根,
也表示函數(shù)g(x)=(a^2-1)x^2+(a-1)x+2/(a+1)的圖像在x軸之上或與x軸相切,
也表示函數(shù)g(x)恒相對(duì)于或等于0
這樣,也就確保了函數(shù)f(x)=√[(a^2-1)x^2+(a-1)x+2/(a+1)]的定義域?yàn)镽
1≤a≤9