b. g(a) = -4 1/4 a - 8 = -4 1/4 a = 4 a = 4 x 4 a = 16
Nomor 5 f(x) = ax + b a. f(1) - f(-3) = f(1) - f(-3) a + b - (-3a + b) = 12 - 8 a + b + 3a - b = 4 4a = 4 a = 1 Lalu, f(1) = 12 a + b = 12 1 + b = 12 b = 12 - 1 b = 11
Maka, a = 1 dan b = 11
b. Sehingga, dapat ditulis: f(x) = 1x + 11 f(x) = x + 11
Memanfaatkan yang telah diketahui:
h(3) - h(-2) = h(3) - h(-2)
3p + q - (-2p + q) = -5 - 10
3p + q + 2p - q = -15
5p = -15
p = -3
Ambil salah satu,
h(3) = -5
3p + q = -5
3(-3) + q = -5
-9 + q = -5
q = -5 + 9
q = 4
Maka, p dan q berturut-turut adalah -3, dan 4
b.
h(3) = 3p + q
h(3) = 3(-3) + 4
h(3) = -9 + 4
h(3) = -5
Nomor 2
Dapat dituliskan seperti ini:
h(x) = 6x - 4
a.
Daerah asal f(x)
x = {-2, -1, 0, 1, 2}
b.
Daerah hasil:
f(-2) = 6(-2) - 4 = -12 - 4 = -16
f(-1) = 6(-1) - 4 = -6 - 4 = -10
f(0) = 6(0) - 4 = 0 - 4 = -4
f(1) = 6(1) - 4 = 6 - 4 = 2
f(2) = 6(2) - 4 = 12 - 4 = 8
Maka,
R = {-16, -10, -4, 2, 8}
Nomor 3
f(x) = ax² + bx + 3
a.
Diketahui:
f(-2) = 9
a(-2)² + b(-2) + 3 = 9
4a - 2b + 3 = 9
4a - 2b = 6
2a - b = 3
f(5) = -12
a(5)² + b(5) + 3 = -12
25a + 5b +3 = -12
25a + 5b = -15
5a + b = -3
Jumlahkan kedua persamaaan:
2a - b = 3
5a + b = -3
Jumlah - - -
7a = 0
a = 0
Dan,
2a - b = 3
2(0) - b = 3
0-b = 3
b = -3
Maka,
Nilai a dan b adalah 0 dan -3
b.
Sehingga,
f(x) = 0x² - 3x + 3
f(x) = -3x + 3
Nomor 4
g(x) = 1/4 x - 8
Maka,
a.
g(4) = 1/4 (4) - 8 = 1 - 8 = -7
g(6) = 1/4 (6) - 8 = 3/2 - 8 = -13/2
b.
g(a) = -4
1/4 a - 8 = -4
1/4 a = 4
a = 4 x 4
a = 16
Nomor 5
f(x) = ax + b
a.
f(1) - f(-3) = f(1) - f(-3)
a + b - (-3a + b) = 12 - 8
a + b + 3a - b = 4
4a = 4
a = 1
Lalu,
f(1) = 12
a + b = 12
1 + b = 12
b = 12 - 1
b = 11
Maka, a = 1 dan b = 11
b.
Sehingga, dapat ditulis:
f(x) = 1x + 11
f(x) = x + 11