Diketahui f(x) = 2x/3-x dan x≠3 Tentukan (fof^-1)(x)

<p>Jawaban : (fof^-1)(x) = x</p><p>&nbsp;</p><p>Ingat kembali:</p><p>(fog)(x) = f(g(x))</p><p>(gof)(x) = g(f(x))</p><p>f(x) = y → f^-1(y) = x</p><p>&nbsp;</p><p>Diketahui: f(x) = (2x) / (3 - x)</p><p>&nbsp;</p><p>Maka:</p><p>f(x) = (2x) / (3 - x)</p><p>y = (2x) / (3 - x)</p><p>y(3 - x) = 2x</p><p>3y - xy = 2x</p><p>2x = 3y - xy</p><p>2x + xy = 3y</p><p>x(2 + y) = 3y</p><p>x = (3y) / (2 + y)</p><p>&nbsp;f^-1(y) = (3y) / (2 + y)</p><p>&nbsp;f^-1(x) = (3x) / (2 + x)</p><p>&nbsp;</p><p>Sehingga:</p><p>(fof^-1)(x) = f(f^-1(x))</p><p>(fof^-1)(x) = f[(3x)/(2 + x)]</p><p>(fof^-1)(x) = 2[(3x)/(2 + x)] / [3 - (3x)/(2 + x)]</p><p>(fof^-1)(x) = [(6x)/(2 + x)] / [(3(2 + x) - 3x) / (2 + x)]&nbsp;</p><p>(fof^-1)(x) = [(6x)/(2 + x)] / [(6)/(2 + x)]</p><p>(fof^-1)(x) = [(6x)/(2 + x)] . [(2 + x)/(6)]</p><p>(fof^-1)(x) = x</p><p>&nbsp;</p><p>Jadi, &nbsp;(fof^-1)(x) = x.</p>