Question

(本小題滿分10分)

已知函數，當點 (x，y) 是函數y = f (x) 圖象上的點時，點是函數y = g(x) 圖象上的點．

(1)    寫出函數y = g (x) 的表達式；

(2)    當g(x)-f (x)0時，求x的取值范圍；

(3)    當x在 (2) 所給范圍內取值時，求的最大值．

 

Answer 1

【答案】

 

（1）

（2）

（3）[g(x)-f (x)]_max=

【解析】

解得0 ≤ x ≤ 1；·········································································· 6分

(3) 當0≤ x≤ 1時，g(x) -f (x) =-log ₂(x+1)，[來源:學&科&網Z&X&X&K]

令，

則kx² + (2k-3)x + (k-1) = 0，························································· 7分

∵x的取值存在，∴D = (2k-3)²-4k(k-1) ≥ 0，

解得：，·········································································· 9分

當k=時，x=∈[0，1]，

∴當x=時，[g(x)-f (x)]_max=．········································· 10分