18. Diketahui fungsi f(x) = x +2/x-5 dan g(x)=2x+3,maka (g•f)-1(x) =...
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18. ( g o f )(x) = g[ f(x) ]
[tex] = g( \frac{x + 2}{x - 5} ) \\ = 2( \frac{x + 2}{x - 5} ) + 3 \\ = \frac{2x + 4}{x - 5} + \frac{3(x - 5)}{x - 5} \\ = \frac{2x + 4 + 3x - 15}{x - 5} \\ = \frac{5x - 11}{x - 5} [/tex]
( g o f)(x) = y
[tex] \frac{5x - 11}{x - 5} = y[/tex]
5x - 11 = y( x - 5 )
5x - 11 = yx - 5y
5x - yx = -5y + 11
( 5 - y ) x = -5y + 11
[tex]x = \frac{ - 5y + 11}{5 - y} \\ (gof) {}^{ - 1} (x) = \frac{ - 5x + 11}{5 - x} [/tex]
[answer.2.content]
