Matematika Diketahui f : R-R[tex]f(x) = \frac{x + 2}{x - 3} [/tex]dan g(x)=3x+1. Fungsi (fog)^-1(x) =​

stephaniarohanulv – March 07, 2023

Diketahui f : R-R
[tex]f(x) = \frac{x + 2}{x - 3} [/tex]
dan g(x)=3x+1. Fungsi (fog)^-1(x) =​

( f o g )(x) = f[ g(x) ]

= f( 3x + 1 )

[tex] = \frac{(3x + 1) + 2}{(3x + 1) - 3} \\ = \frac{3x + 3}{3x - 2} [/tex]

( f o g )(x) = y

[tex] \frac{3x + 3}{3x - 2} = y[/tex]

3x + 3 = y( 3x - 2 )

3x + 3 = 3yx - 2y

3x - 3yx = -2y - 3

( 3 - 3y ) x = -2y - 3

[tex]x = \frac{ - 2y - 3}{3 - 3y} \\ (fog) {}^{ - 1} (x) = \frac{ - 2x - 3}{3 - 3x} [/tex]

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