Diketahui f : R —> R dan g: R —> R dengan g(x) = (3x-1)/(x+2) dan (fog)(x) = (x-5)/(x+2). Dengan demikian maka f(x+1) = .. A. x - 2 B. x - 1 C. x + 1 D. x + 2 E. x + 3

<p>Jawaban: &nbsp;f(x+1) = 7/5</p><p>&nbsp;</p><p>Ingat konsep berikut ini:</p><p>(f o g)(x) = f(g(x))</p><p>&nbsp;</p><p>g(x) = (3x-1)/(x+2)</p><p>(fog)(x) = (x-5)/(x+2)</p><p>f(g(x)) = (x-5)/(x + 2)</p><p>f((3x-1)/(x+2)) = (x-5)/(x + 2)</p><p>&nbsp;</p><p>misal:</p><p>(3x-1)/(x+2) = a</p><p>a(x+2) = 3x - 1</p><p>ax + 2a = 3x - 1</p><p>ax - 3x = -2a - 1</p><p>x(a - 3) = -2a - 1</p><p>x = (-2a - 1)/(a - 3)</p><p>f(x) = [((-2x-1)/(x-3)) - 5]/[((-2x-1)/(x-3)) -3]</p><p>f(x) = [((-2x-1)-(x-3)5)/(x-3)]/[((-2x-1)-(x-3)3)/(x-3)]</p><p>f(x) = (-2x - 1 - (5x - 15))/(-2x - 1 - (3x - 9))</p><p>f(x) = (-2x - 1 - 5x + 15)/(-2x - 1 - 3x - 9)</p><p>f(x) = (-7x + 14)/(-5x + 10)</p><p>f(x+1) = (-7(x+1) + 14)/(-5(x+1) + 10)</p><p>f(x+1) = (-7x-7+14)/(-5x-5+10)</p><p>f(x+1) = (-7x + 7)/(-5x + 5)</p><p>f(x+1) = (-7(x-1))/(-5(x-1))</p><p>f(x+1) = 7/5</p><p>&nbsp;</p><p>Jadi, f(x+1) = 7/5.</p>