Question

(本小题满分10分)

已知函数，当点 (x，y) 是函数y = f (x) 图象上的点时，点是函数y = g(x) 图象上的点．

(1)    写出函数y = g (x) 的表达式；

(2)    当g(x)-f (x)0时，求x的取值范围；

(3)    当x在 (2) 所给范围内取值时，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) 当0≤ x≤ 1时，g(x) -f (x) =-log ₂(x+1)，[来源:学&科&网Z&X&X&K]

令，

则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

当k=时，x=∈[0，1]，

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