Fungsi f(x) dan g(x) didefinisikan dengan f(x) = (2×+3)/(x-5), g(x) = 3x+5. Jika (fog)(x)–1 (a) = (19)/(3), maka nilai dari a adalah

<p>Nilai a adalah <strong>2,68 ≈ 3&nbsp;</strong></p><p>&nbsp;</p><p><strong>Diketahui :</strong></p><ul><li>f(x) = ^{(2x + 3)}/_{(x - 5)}</li><li>g(x) = 3x + 5</li><li>(f o g)-¹(a) = ¹⁹/₃</li></ul><p><strong>Ditanya : </strong>a = ... ?</p><p><strong>Dijawab :</strong></p><p>• Mencari (f o g)(x) = ... ?</p><p>(f o g)(x) = f(g(x))</p><p>(f o g)(x) = f(3x + 5)</p><p>(f o g)(x) = ^{(2(3x + 5) + 3)}/_{(3x + 5) - 5)}</p><p>(f o g)(x) = ^{(6x + 10 + 3)}/_3x</p><p>(f o g)(x) = ^{(6x + 13)}/_3x</p><p>&nbsp;</p><p>• Ubah (f o g)(x) menjadi (f o g)-¹(x)&nbsp;</p><p>(f o g)(x) = ^{(ax + b)}/_{(cx + d)} → menjadi&nbsp;</p><p>→ (f o g)-¹(x) = ^{(-dx + b)}/_{(cx - a)}&nbsp;</p><p>(f o g)(x) = ^{(6x + 13)}/_3x → a = 6, b = 13, c = 3, d = 0</p><p>(f o g)-¹(x) = ^{(-0x + 13)}/_{(3x - 6)}&nbsp;</p><p>(f o g)-¹(x) = ¹³/_{(3x - 6)}&nbsp;</p><p>&nbsp;</p><p>• Mencari nilai a = ... ?</p><p>(f o g)-¹(x) = 13/(3x - 6)&nbsp;</p><p>(f o g)-¹(a) = ¹³/_{(3a - 6)}&nbsp;</p><p>^{&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 19}/₃= ¹³/_{(3a - 6)}&nbsp;</p><p>19(3a - 6) = 13 × 3</p><p>&nbsp;57a - 114 = 39</p><p>57a = 39 + 114</p><p>57a = 153</p><p>a = ¹⁵³/₅₇ = 2,68 ≈ 3</p><p>&nbsp;</p><p>Selesai :')🙏</p>