Suci A
31 Mei 2024 07:50
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Suci A
31 Mei 2024 07:50
Pertanyaan
Jika diketahui f(g(x)) = (11x + 2)/(3x - 1) dan f(x) = 2x + 3 maka tentukan g(x)
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Andrew F
31 Mei 2024 08:50
<p>f(g(x)) = (11x + 2)/(3x - 1)</p><p>f(x) = 2x + 3</p><p>g(x) = ...</p><p> </p><p>Maka :</p><p>g(x) = a</p><p> </p><p>f(x) = 2x + 3</p><p>f(a) = 2(a) + 3 = (11x + 3)/(3x - 1)</p><p>----------------------------------------------------- × (3x - 1)</p><p>(2a)(3x - 1) + (3)(3x - 1) = (11x + 3)</p><p>(2a × 3x) + (2a × (-1)) + (3 × 3x) + (3 × (-1)) = 11x + 3</p><p>6ax - 2a + 9x - 3 = 11x + 3</p><p>a(6x - 2) = 11x - 9x + 3 + 3</p><p>a(6x - 2) = 2x + 6</p><p>a = 2x/(6x - 2) + 6/(6x - 2)</p><p>a = (2x + 6)/(6x - 2)</p><p>g(x) = (2x + 6)/(6x - 2).</p><p> </p><p>Jadi, g(x) = (2x + 6)/(6x - 2).</p><p> </p><p>Semoga membantu.</p>
f(g(x)) = (11x + 2)/(3x - 1)
f(x) = 2x + 3
g(x) = ...
Maka :
g(x) = a
f(x) = 2x + 3
f(a) = 2(a) + 3 = (11x + 3)/(3x - 1)
----------------------------------------------------- × (3x - 1)
(2a)(3x - 1) + (3)(3x - 1) = (11x + 3)
(2a × 3x) + (2a × (-1)) + (3 × 3x) + (3 × (-1)) = 11x + 3
6ax - 2a + 9x - 3 = 11x + 3
a(6x - 2) = 11x - 9x + 3 + 3
a(6x - 2) = 2x + 6
a = 2x/(6x - 2) + 6/(6x - 2)
a = (2x + 6)/(6x - 2)
g(x) = (2x + 6)/(6x - 2).
Jadi, g(x) = (2x + 6)/(6x - 2).
Semoga membantu.
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