MATHS 一問

一些簡單例子: f(x) = x²
g(x) = x³f[g(x)] = (x³)²
g[f(x)] = (x²)³

∴ f[g(x)] = g[f(x)] = x⁶
************************************* f(x) = x + F
g(x) = x + G
(F ≠ G)f[g(x)] = (x + G) + F = x + G + F
g[f(x)] = (x + F) + G = x + F + G

∴ f[g(x)] = g[f(x)] = x + G + F

2012-08-04 12:00:19 補充：
上面是不同的例子。
符合要求的答案是無窮的,再舉一個更簡單的例子:

若 f(x) = x
則 g(x) 可為除 g(x) = x 外的任何函數。

因為
f[g(x)] = g(x)
g[f(x)] = g(x)

因為有2個例子,2個都不同函數= =