Penjelasan dengan langkah-langkah:
[tex](fog)(x) = f(g(x)) = f( \frac{x + 2}{x - 1} ) \\ = ( \frac{x + 2}{x - 1} )x - 3 \\ = \frac{ {x}^{2} + 2x }{x - 1} - 3 \\ = \frac{ {x}^{2} + 2x}{x} - \frac{3x}{x} \\ = \frac{ {x}^{2} - x}{x} \\ = x \frac{(x - 1)}{x} \\ = x - 1[/tex]
[tex](gof)(x) = g(f(x)) = g(2x - 1) \\ = \frac{(2x - 3) + 2}{(2x - 3) - 1} \\ = \frac{2x - 1}{2x - 4} [/tex]
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Penjelasan dengan langkah-langkah:
[tex](fog)(x) = f(g(x)) = f( \frac{x + 2}{x - 1} ) \\ = ( \frac{x + 2}{x - 1} )x - 3 \\ = \frac{ {x}^{2} + 2x }{x - 1} - 3 \\ = \frac{ {x}^{2} + 2x}{x} - \frac{3x}{x} \\ = \frac{ {x}^{2} - x}{x} \\ = x \frac{(x - 1)}{x} \\ = x - 1[/tex]
[tex](gof)(x) = g(f(x)) = g(2x - 1) \\ = \frac{(2x - 3) + 2}{(2x - 3) - 1} \\ = \frac{2x - 1}{2x - 4} [/tex]