Jika fungsi f(x)=2x-1/3x ; x ≠ 0 dan (fog)(x) = 4x - 7, tentukanlah g(x).
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Jawaban Singkat
[tex]g(x)=\frac{1}{23-12x}[/tex]
Penjabaran
[tex]f(x)=\frac{2x-1}{3x}\ ;\ x\neq 0\\\\(f\ o\ g)(x)=4x-7[/tex]
Mencari g(x):
[tex](f\ o\ g)(x) = f(g(x))\\\\\frac{2(g(x))-1}{3(g(x))} =4x-7\\\\(2(g(x))-1)=(4x-7)(3(g(x)))\\\\2(g(x))-1=12x(g(x))-21(g(x))\\\\2(g(x))+21(g(x))-12x(g(x))=1\\\\23(g(x))-12x(g(x))=1\\\\g(x)(23-12x)=1\\\\g(x)=\frac{1}{23-12x}[/tex]
