Question

若函數(shù)f(x)＝的圖象如圖，則m的取值范圍是________．

Answer 1

(1,2)

∵函數(shù)f(x)的定義域?yàn)镽，∴x²＋m恒不等于零，∴m＞0.由題圖知，當(dāng)x＞0時(shí)，f(x)＞0，∴2－m＞0⇒m＜2.又∵在(0，＋∞)上函數(shù)f(x)在x＝x₀(x₀＞1)處取得最大值，而f(x)＝，∴x₀＝＞1⇒m＞1.綜上，1＜m＜2.