Diketahui g (x) =3x-1 per x dan (gof^-1) (x) =3x-6 per x-1 tentukan a. F (x) b. (Fog) ^-1 (x)

[tex]g(x) = 3x - 1 \\ (gof) ^{ - 1} (x) = \frac{3x - 6}{x - 1} \\ \\ y = \frac{3x - 6}{x - 1} \\ y \times (x - 1) = 3x - 6 \\ yx - y = 3x - 6 \\ yx - 3x = - 6 + y \\ x = \frac{ - 6 + y}{y - 3} \\ \\ (gof)(x) = \frac{ - 6 + x}{x - 3} = 3f(x) - 1 \\ 3f(x) = \frac{ - 6 + x + x - 3}{x - 3} = \frac{2x - 9}{x - 3} \\ f(x) = \frac{2x - 9}{3x - 9} \\ \\ fog(x) = \frac{2 \frac{3x - 1}{x} - 9 }{3 \frac{3x - 1}{x} - 9} \\ = \frac{ \frac{6x - 2}{x} - \frac{9x}{x} }{ \frac{9x - 3}{x} - \frac{9x}{x} } = \frac{ - 3x - 2}{x} \times \frac{x}{ - 3} \\ = \frac{ 3x + 2}{3} \\ \\ y = \frac{ 3x + 2}{3} \\ 3x = 3y - 2 \\ x = \frac{3y - 2}{3 } \\ \\ (fog) ^{ - 1} (x) = \frac{3x - 2}{3 }[/tex]