Almira D
15 Januari 2023 02:24
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Almira D
15 Januari 2023 02:24
Pertanyaan
Nilai dari (2f+g)(-3) dari bentuk berikut adalah... * f(2 x+1)=4 x^(2)+10 x-3 g(3 x-2)=(1-6x)/(3 x+2)
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W. Lestari
Mahasiswa/Alumni Universitas Sriwijaya
08 Februari 2023 02:56
<p>Jawaban : -13</p><p> </p><p>Ingat kembali:</p><p>(f + g)(x) = f(x) + g(x)</p><p>(k.f)(x) = k . f(x)</p><p> </p><p>Diketahui: f(2x + 1) = 4x<sup>2</sup> + 10x - 3 dan g(3x - 2) = (1 - 6x)/(3x + 2)</p><p> </p><p>Maka:</p><p>f(2x + 1) = 4x<sup>2</sup> + 10 x - 3 → misalkan : 2x + 1 = A → x = (A - 1)/2</p><p>f(A) = 4[(A - 1)/2]<sup>2</sup> + 10[(A - 1)/2] - 3</p><p>f(A) = 4[(A<sup>2</sup> - 2A + 1)/4] + 5(A - 1) - 3</p><p>f(A) = A<sup>2</sup> - 2A + 1 + 5A - 5 - 3</p><p>f(A) = A<sup>2</sup> + 3A - 7</p><p>f(x) = x<sup>2</sup> + 3x - 7</p><p> </p><p>g(3x - 2) = (1 - 6x)/(3x + 2) → misalkan: 3x - 2 = P → x = (P + 2)/3</p><p>g(P) = [1 - 6 . (P+2)/3] / [3 . (P + 2)/3 + 2]</p><p>g(P) = [1 - 2(P + 2)] / [(P + 2) + 2]</p><p>g(P) = (1 - 2P - 4)/(P + 2 + 2)</p><p>g(P) = (-3 - 2P)/(P + 4)</p><p>g(x) = (-3 - 2x)/(x + 4)</p><p> </p><p>Sehingga:</p><p>(2f + g)(x) = 2 . f(x) + g(x)</p><p>(2f + g)(x) = 2 . (x<sup>2</sup> + 3x - 7) + [(-3 - 2x)/(x + 4)]</p><p>(2f + g)(x) = 2x<sup>2</sup> + 6x - 14 + [(-3 - 2x)/(x + 4)]</p><p>(2f + g)(-3) = 2(-3)<sup>2</sup> + 6(-3) - 14 + [(-3 - 2(-3))/((-3) + 4)]</p><p>(2f + g)(-3) = 2(9) - 18 - 14 + [(-3 + 6)/(-3 + 4)]</p><p>(2f + g)(-3) = 18 - 18 - 14 + (3/1)</p><p>(2f + g)(-3) = 18 - 18 - 14 + 1</p><p>(2f + g)(-3) = -13</p><p> </p><p>Jadi, (2f + g)(-3) = -13.</p>
Jawaban : -13
Ingat kembali:
(f + g)(x) = f(x) + g(x)
(k.f)(x) = k . f(x)
Diketahui: f(2x + 1) = 4x2 + 10x - 3 dan g(3x - 2) = (1 - 6x)/(3x + 2)
Maka:
f(2x + 1) = 4x2 + 10 x - 3 → misalkan : 2x + 1 = A → x = (A - 1)/2
f(A) = 4[(A - 1)/2]2 + 10[(A - 1)/2] - 3
f(A) = 4[(A2 - 2A + 1)/4] + 5(A - 1) - 3
f(A) = A2 - 2A + 1 + 5A - 5 - 3
f(A) = A2 + 3A - 7
f(x) = x2 + 3x - 7
g(3x - 2) = (1 - 6x)/(3x + 2) → misalkan: 3x - 2 = P → x = (P + 2)/3
g(P) = [1 - 6 . (P+2)/3] / [3 . (P + 2)/3 + 2]
g(P) = [1 - 2(P + 2)] / [(P + 2) + 2]
g(P) = (1 - 2P - 4)/(P + 2 + 2)
g(P) = (-3 - 2P)/(P + 4)
g(x) = (-3 - 2x)/(x + 4)
Sehingga:
(2f + g)(x) = 2 . f(x) + g(x)
(2f + g)(x) = 2 . (x2 + 3x - 7) + [(-3 - 2x)/(x + 4)]
(2f + g)(x) = 2x2 + 6x - 14 + [(-3 - 2x)/(x + 4)]
(2f + g)(-3) = 2(-3)2 + 6(-3) - 14 + [(-3 - 2(-3))/((-3) + 4)]
(2f + g)(-3) = 2(9) - 18 - 14 + [(-3 + 6)/(-3 + 4)]
(2f + g)(-3) = 18 - 18 - 14 + (3/1)
(2f + g)(-3) = 18 - 18 - 14 + 1
(2f + g)(-3) = -13
Jadi, (2f + g)(-3) = -13.
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