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Jawaban: soal-soal komposisi fungsi ini. Diketahui: - f(x) = 2x + 5- g(x) = x - 5 Kita akan menyelesaikan: a. (g o f)(x) dan (f o g)(x)b. (g o f)⁻¹(x) dan (f o g)⁻¹(x)c. f⁻¹(x) dan g⁻¹(x)d. (g⁻¹ o f⁻¹)(x) dan (f⁻¹ o g⁻¹)(x) a. (g o f)(x) dan (f o g)(x) - (g o f)(x) = g(f(x))- g(f(x)) = g(2x + 5)- = (2x + 5) - 5- = 2x- (f o g)(x) = f(g(x))- f(g(x)) = f(x - 5)- = 2(x - 5) + 5- = 2x - 10 + 5- = 2x - 5 b. (g o f)⁻¹(x) dan (f o g)⁻¹(x) - (g o f)⁻¹(x):- Karena (g o f)(x) = 2x, misalkan y = 2x- x = y/2- Jadi, (g o f)⁻¹(x) = x/2- (f o g)⁻¹(x):- Karena (f o g)(x) = 2x - 5, misalkan y = 2x - 5- y + 5 = 2x- x = (y + 5) / 2- Jadi, (f o g)⁻¹(x) = (x + 5) / 2 c. f⁻¹(x) dan g⁻¹(x) - f⁻¹(x):- Misalkan y = 2x + 5- y - 5 = 2x- x = (y - 5) / 2- Jadi, f⁻¹(x) = (x - 5) / 2- g⁻¹(x):- Misalkan y = x - 5- y + 5 = x- Jadi, g⁻¹(x) = x + 5 d. (g⁻¹ o f⁻¹)(x) dan (f⁻¹ o g⁻¹)(x) - (g⁻¹ o f⁻¹)(x) = g⁻¹(f⁻¹(x))- g⁻¹(f⁻¹(x)) = g⁻¹((x - 5) / 2)- = ((x - 5) / 2) + 5- = (x - 5 + 10) / 2- = (x + 5) / 2- (f⁻¹ o g⁻¹)(x) = f⁻¹(g⁻¹(x))- f⁻¹(g⁻¹(x)) = f⁻¹(x + 5)- = ((x + 5) - 5) / 2- = x / 2 Ringkasan Jawaban: - a. (g o f)(x) = 2x, (f o g)(x) = 2x - 5- b. (g o f)⁻¹(x) = x/2, (f o g)⁻¹(x) = (x + 5) / 2- c. f⁻¹(x) = (x - 5) / 2, g⁻¹(x) = x + 5- d. (g⁻¹ o f⁻¹)(x) = (x + 5) / 2, (f⁻¹ o g⁻¹)(x) = x / 2maaf cuman bisa bantu segitu,memori penuh

Answered by ara1412 | 2025-08-19