YR
Yolla R
28 November 2023 11:08
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YR
Yolla R
28 November 2023 11:08
Pertanyaan
Diketahui f(x) = 3/x, g(x) = x-4 jika (fog)(a) = (gof)(a). Tentukan nilai a?
Diketahui f(x) = 3/x, g(x) = x-4 jika (fog)(a) = (gof)(a). Tentukan nilai a?
44
1
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LL
Laila L
28 November 2023 11:42
Jawaban terverifikasi
<p>fog(a) = gof(a)</p><p>3/(x-4) = (3/x)-4</p><p>3/(x-4) = (3-4x)/x</p><p>3x = (x-4)(3-4x)</p><p>3x = 3x-4x²-12+16x</p><p>3x = 4x²-19x+12</p><p>0 = 4x²-22x+12</p><p>0 = 2x²-11x+6</p><p>0 = (2x+1)(x-6)</p><p>=>2x+1 = 0</p><p> x = -1/2</p><p>=>x-6 = 0</p><p> x = 6</p><p>=>x = a = -1/2 atau 6</p>
fog(a) = gof(a)
3/(x-4) = (3/x)-4
3/(x-4) = (3-4x)/x
3x = (x-4)(3-4x)
3x = 3x-4x²-12+16x
3x = 4x²-19x+12
0 = 4x²-22x+12
0 = 2x²-11x+6
0 = (2x+1)(x-6)
=>2x+1 = 0
x = -1/2
=>x-6 = 0
x = 6
=>x = a = -1/2 atau 6
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