已知f(x)為一線型函數，f(1):f(2)=3:4,則f(4):f(8)=? 誰可以教教我這題?
回答 (2)
2017-12-04 9:43 pm
f(x)=線型函數 => f(x)=ax+b
f(1):f(2)=3:4
a+b 3
=> -------- = ----
2a+b 4
=> 4(a+b) = 3(2a+b)
=> 4a+4b = 6a+3b
=> b = 2a
4a+b 4a+2a 6a 3
∴ f(4):f(8) = ---------- = ----------- = ----- = ---
8a+b 8a+2a 10a 5
f(1):f(2)=3:4
a+b 3
=> -------- = ----
2a+b 4
=> 4(a+b) = 3(2a+b)
=> 4a+4b = 6a+3b
=> b = 2a
4a+b 4a+2a 6a 3
∴ f(4):f(8) = ---------- = ----------- = ----- = ---
8a+b 8a+2a 10a 5
2017-12-03 6:30 pm
Sol
f(x)=ax+b
f(1)：f(2)=3：4
4f(1)=3f(2)
f(1)=a+b
f(2)=2a+b
4(a+b)=3(2a+b)
4a+4b=6a+3b
b=2a
f(4)=4a+b=4a+2a=6a
f(8)=8a+b=8a+2a=10a
(1) a=0
f(x)=b (不合)
(2) a<>0
f(4)：f(8)=6a：10a=3：5
f(x)=ax+b
f(1)：f(2)=3：4
4f(1)=3f(2)
f(1)=a+b
f(2)=2a+b
4(a+b)=3(2a+b)
4a+4b=6a+3b
b=2a
f(4)=4a+b=4a+2a=6a
f(8)=8a+b=8a+2a=10a
(1) a=0
f(x)=b (不合)
(2) a<>0
f(4)：f(8)=6a：10a=3：5
收錄日期: 2021-04-30 22:35:44
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20171203075120AAXoHqF