tentukan (fog)¹(x) dan (gof)¹ (x) dari fungsi berikut ini. f(x)=2×+3 dan g(x)=x-1

Halo Gina :D Jawaban: (fog)⁻¹(x) = (x - 1)/2 (gof)⁻¹(x) = (x - 2)/2 Perhatikan konsep fungsi komposisi berikut: (f o g)(x) = f(g(x)) (g o f)(x) = g(f(x)) Perhatikan juga konsep fungsi invers berikut: f(x) = y maka invers fungsinya: f^(-1) (y) = x Diketahui: f(x) = 2x + 3 g(x) = x-1 Ditanya: asumsi (fog)⁻¹(x) = ....? (gof)⁻¹(x) = ....? Pembahasan: (f o g)(x) = f(g(x)) (f o g)(x) = 2(g(x)) + 3 (f o g)(x) = 2(x-1) + 3 (f o g)(x) = 2(x) + 2(-1) + 3 (f o g)(x) = 2x - 2 + 3 (f o g)(x) = 2x + 1 (f o g)(x) = y 2x + 1 = y 2x = y - 1 x = (y - 1)/2 (fog)⁻¹(y) = x (fog)⁻¹(y) = (y - 1)/2 (fog)⁻¹(x) = (x - 1)/2 (g o f)(x) = g(f(x)) (g o f)(x) = (f(x)) - 1 (g o f)(x) = (2x + 3) - 1 (g o f)(x) = 2x + 3 - 1 (g o f)(x) = 2x + 2 (g o f)(x) = y 2x + 2 = y 2x = y - 2 x = (y - 2)/2 (gof)⁻¹(y) = x (gof)⁻¹(y) = (y - 2)/2 (gof)⁻¹(x) = (x - 2)/2 Jadi, kesimpulan jawaban: (fog)⁻¹(x) = (x - 1)/2 (gof)⁻¹(x) = (x - 2)/2