If __f(2x)=8x^3 + 4x, then f(3a) = ?
我要詳解, 唔該!
math ce 一問 1985 MC Q40 (20點)
2007-06-10 6:56 am
回答 (3)
2007-06-10 7:00 am
✔ 最佳答案
f(2x)=8x^3 + 4xf(2x)=(2x)^3 + 2(2x)
Replace 2x by x,
f(x) = x^3 + 2x
f(3a) = (3a)^3 + 2(3a)
= 27a^3 + 6a
參考: My Maths Knowledge
2007-06-10 10:33 am
Put x = 1.5a,
so 2x = 3a and hence f(2x) = f(3a)
Now, x^3 = (1.5a)^3 = 1.5^3 a^3 = 3.375a^3
4x = 6a
Therefore
f(2x) = 8x^3 + 4x becomes
f(3a) = 8(3.375a^3) + 6a = 27a^3 + 6a = 3a (9a^2 +2)
so 2x = 3a and hence f(2x) = f(3a)
Now, x^3 = (1.5a)^3 = 1.5^3 a^3 = 3.375a^3
4x = 6a
Therefore
f(2x) = 8x^3 + 4x becomes
f(3a) = 8(3.375a^3) + 6a = 27a^3 + 6a = 3a (9a^2 +2)
2007-06-10 8:14 am
f(3a) = f(2* (3a/2))
= 8(3a/2)^3 + 4(3a/2)
= 8 (27/8)a^3 + 6a
= 27a^3 + 6a
= 8(3a/2)^3 + 4(3a/2)
= 8 (27/8)a^3 + 6a
= 27a^3 + 6a
參考: me
收錄日期: 2021-04-13 13:47:01
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