F.4 數學 ( 函數 )

[匿名]

2010-10-18 1:39 am

1. 若 f ( x ) = 3 ( 2 ^3x )，求下列各值。
(a) f ( 0 )
(b) f ( - 2 / 3 )

2. 若 g ( x ) = sin ( x + 10° ) ，其中 0 ° ≦ x ≦ 80 °，求下列各值。
(a) 2g ( 20 ° ) + g ( 80 ° )
(b) √2g ( 35 ° ) + √3g ( 50 ° )

3. 若 H ( x ) = 4x^2 - 8x + 1，求
(a) H ( p / 2 )；
(b) H ( q + 2 )。

4. 若 f ( x ) = x^2 - kx + 6 及 f ( 2 ) = f ( 3 )，求 k 的值。

回答 (1)

用戶87381

2010-10-18 2:41 am

✔ 最佳答案

1a) f(0) = 3(2^3*0) = 3(2^0) = 3(1) = 3
b) f(-2/3) = 3(2^3*-2/3) = 3(2^-2) = 3(1/4) = 3/4

2a) 2g ( 20 ° ) + g ( 80 ° )
=2sin(20°+10°)+sin(80°+10°)
=2sin30°+sin90°
=2(0.5)+1
=2
b) √2g ( 35 ° ) + √3g ( 50 ° )
=√2sin(35°+10°)+√3sin(50°+10°)
=(√2)(1/√2)+(√3)(√3/2)
=1+3/2
=5/2

3a) H(p/2) = 4(p/2)^2-8(p/2)+1 = 4(p^2/4)-8(p/2)+1 = p^2-4p+1
b) H(q+2) = 4(q+2)^2-8(q+2)+1 = 4(q^2+4q+4)-8q-16+1
= 4q^2+16q+16-8q-16+1 = 4q^2+8q+1

4. f(2) = f(3)
2^2-k(2)+6 = 3^2-k(3)+6
10-2k = 15-3k
k = 5

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