GWD 19-02

[harass]

For which of the following functions f is f(x) = f(1-x) for all x?

A. f(x) = 1 - x
B. f(x) = 1 - x2
C. f(x) = x2 - (1-x)2
D. f(x) = x2(1-x)2
E. f(x) = x / (1-x)
Answer: D

不懂題目在問什麼?
所以也不懂答案為什麼是那一個?
謝謝

[zazer.lin]

不好意思...小弟先幫您更新一下題目...

For which of the following functions f is f(x) = f(1-x) for all x?

A. f(x) = 1 - x
B. f(x) = 1 - x[sup]2[/sup]
C. f(x) = x[sup]2[/sup] - (1-x)[sup]2[/sup]
D. f(x) = x[sup]2[/sup](1-x)[sup]2[/sup]
E. f(x) = x / (1-x)
Answer: D

不懂題目在問什麼?
所以也不懂答案為什麼是那一個?
謝謝

A. f(x) = 1-x ==> f(1-x) = 1 - (1-x) = x =\= 1 - x = f(x)

B. f(x) = 1 - x[sup]2[/sup] ==> f(1-x) = 1 - (1-x)[sup]2[/sup] = 2x - x[sup]2[/sup] =\= 1-x[sup]2[/sup] = f(x)

C. f(x) = x[sup]2[/sup] - (1-x)[sup]2[/sup] ==> f(1-x) = (1-x)[sup]2[/sup] - [1 - (1-x)][sup]2[/sup] = (1-x) [sup]2[/sup] -x[sup]2[/sup] =\= x[sup]2[/sup] - (1-x)[sup]2[/sup] = f(x)

D. f(x) = x[sup]2[/sup](1 - x)[sup]2[/sup] ==> f(1-x) = (1-x)[sup]2[/sup][1 - (1-x)][sup]2[/sup] = (1 - x)[sup]2[/sup]x[sup]2[/sup] = f(x)

E. f(x) = x / (1-x) ==> f(1-x) = (1-x)/[1 - (1-x)] = (1-x)/x =\= x / (1-x) = f(x)

小弟遇到這種問題都是乖乖的代入檢驗, 把選項中所有 x 的地方都換成 1-x, 通常這樣的題目式子都不會很複雜, 有耐心一點大都可以算對. 一點資訊, 供您參考.