Tentukan (fog)¹(x) dan (gof)¹(x) dari fungsi berikut ini. f(x)=12x-4 dan g(x)=5-7x

Jawaban: (f o g)-¹ (x) = -(x + 56)/(84) (g o f)-¹ (x) = -(x - 33)/(84) perhatikan konsep fungsi komposisi berikut: (f o g)(x) = f(g(x)) perhatikan juga konsep invers fungsi berikut: (f o g)(x) = y (f o g)-¹ (y) = x DIketahui: f(x) = 12x - 4 g(x) = 5 - 7x Ditanya: asumsi (fog)-¹(x) = ... ? (gof)-¹(x) = ... ? Pembahasan: (f o g)(x) = f(g(x)) (f o g)(x) = 12(g(x)) - 4 (f o g)(x) = 12(5 - 7x) - 4 (f o g)(x) = 12(5) + 12(-7x) - 4 (f o g)(x) = 60 - 84x - 4 (f o g)(x) = -84x - 56 (f o g)(x) = y -84x - 56 = y -84x = y + 56 x = (y + 56)/(-84) (f o g)-¹ (y) = x (f o g)-¹ (y) = (y + 56)/(-84) (f o g)-¹ (x) = (x + 56)/(-84) (f o g)-¹ (x) = -(x + 56)/(84) (g o f)(x) = g(f(x)) (g o f)(x) = 5 - 7(f(x)) (g o f)(x) = 5 - 7(12x - 4) (g o f)(x) = 5 - 7(12x) - 7(-4) (g o f)(x) = 5 - 84x + 28 (g o f)(x) = -84x + 33 (g o f)(x) = y -84x + 33 = y -84x = y - 33 x = (y - 33)/(-84) (g o f)-¹ (y) = x (g o f)-¹ (y) = (y - 33)/(-84) (g o f)-¹ (x) = (x - 33)/(-84) (g o f)-¹ (x) = -(x - 33)/(84) Jadi, jawabannya: (f o g)-¹ (x) = -(x + 56)/(84) (g o f)-¹ (x) = -(x - 33)/(84)