PP-T1-PS-63

[christinehsu]

63. 7612-!-item-!-187;#058&005607
For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b ?

(A) f(x) = x 2
(B) f(x) = x + 1
(C) f(x) = √x
(D) f(x) = x/2
(E) f(x) = -3x

the answer is (E)

D選項也符合 f(a + b) = f(a) + f(b)
F(1)=1/2 f(3)=f(1+2)=3/2=1/2+2/2

E選項也符合

請問思路哪裡有問題?

[larry.tw]

我覺得D可能選項有錯......

[christinehsu]

所以說先不論答案為何，這樣的思路是正確的嗎?
唉....只要碰到函數問題，整個一個頭兩個大..

[larry.tw]

其實就把題目帶進去而已,不建議代數字(他又沒說一定是正整數,你怎麼只代正整數,那分數呢?)
這題代數字是剛好也對了

f(a + b) = f(a) + f(b)

(D) f(x) = x/2
f(a+b) = (a+b)/2
f(a) = a/2
f(b) = b/2
上面兩個相加也是(a+b)/2 ,所以我說選項可能有錯!!

(E) f(x) = -3x
f(a+b) = -3(a+b)
f(a) = -3a
f(b) = -3b
上面兩個相加也是-3(a+b)

[iamsmall]

f(a + b) = f(a) + f(b)

(D) f(x) = x/2
f(a+b) = (a+b)/2
f(a) = a/2
f(b) = b/2
上面兩個相加也是(a+b)/2 ,所以我說選項可能有錯!!

sorry
我確認之後，D選項是2/x