已知 f(x-3)= 3x^2 - 16x+ 23
(a)求 f(-1)
(b)求 f(x)
數學 math!!!!!!!!! help!!!!!!!!
2008-04-01 5:32 pm
回答 (2)
2008-04-01 5:42 pm
✔ 最佳答案
(a) f(-1) = f(2 - 3)= 3(2)2 - 16(2) + 23
= 12 - 32 + 23
= 3
(b) f(x - 3) = 3x2 - 16x + 23
= 3(x2 - 6x + 9) - 16x + 23 + 18x - 27
= 3(x - 3)2 + 2x - 4
= 3(x - 3)2 + 2(x - 3) - 4 + 6
= 3(x - 3)2 + 2(x - 3) + 2
So,
f(x) = 3x2 + 2x + 2
參考: My Maths knowledge
2008-04-01 9:15 pm
我覺得001 既a)既解答好好,但點解b)又咁樣....
佢可能想俾兩種方法你睇睇@@"
其實數學係要講求精簡快速...為何唔ab兩題都用簡單d既方法?
a) f(-1)=f(2-3)
=3(2^2)-16(2)+23
=12-32+23
=3
b) f(x)=f[(x+3)-3]
=3(x+3)^2-16(x+3)+23
=3(x^2+6x+9)-16x-48+23
=3x^2+2x+2
兩條都用直接代入x既方法~唔係快得多嗎?
仲有一種方法.......就係用001答既方法做左b 先,再用b既答案直接代入-1黎做a 既問題....
佢可能想俾兩種方法你睇睇@@"
其實數學係要講求精簡快速...為何唔ab兩題都用簡單d既方法?
a) f(-1)=f(2-3)
=3(2^2)-16(2)+23
=12-32+23
=3
b) f(x)=f[(x+3)-3]
=3(x+3)^2-16(x+3)+23
=3(x^2+6x+9)-16x-48+23
=3x^2+2x+2
兩條都用直接代入x既方法~唔係快得多嗎?
仲有一種方法.......就係用001答既方法做左b 先,再用b既答案直接代入-1黎做a 既問題....
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