Diketahui f(x) = x + 5, g(x) = 2x + 3, dan h(x) = x + 3x – 2. Tentukan: (h • g • f)(-8) (f • h • g)(-2)

Halo Annabiila. Terima kasih sudah bertanya di Roboguru. Jawaban : a. (hogof)(-8) = -2 b. (fogoh)(-2) = 0 Perhatikan penjelasan berikut ya. Ingat kembali pada komposisi fungsi f(x) dan g(x) berlaku: (fog)(x) = f(g(x)) (gof)(x) = g(f(x)) Diketahui: f(x) = x + 5, g(x) = 2x + 3, dan h(x) = x² + 3x - 2 Ditanya : a. (hogof)(-8) = ... ? b. (fogoh)(-2) = ... ? Maka: a. (hogof)(-8) (gof)(x) = g(f(x)) (gof)(x) = g(x+5) (gof)(x) = 2(x+5) + 3 (gof)(x) = 2x + 10 + 3 (gof)(x) = 2x + 13 (hogof)(x) = h((gof)(x) (hogof)(x) = h(2x+13) (hogof)(x) = (2x+13)² + 3(2x+13) - 2 (hogof)(x) = 4x² + 52x + 169 + 6x + 39 - 2 (hogof)(x) = 4x² + 58x + 206 (hogof)(-8) = 4(-8)² + 58(-8) + 206 (hogof)(-8) = 4(64) - 464 + 206 (hogof)(-8) = 256 - 464 + 206 (hogof)(-8) = -2 Jadi, (hogof)(-8) = -2. b. (fogoh)(-2) (fog)(x) = f(g(x)) (fog)(x) = f(2x+3) (fog)(x) = (2x + 3) + 5 (fog)(x) = 2x + 3 + 5 (fog)(x) = 2x + 8 (fogoh)(x) = (fog)(h(x)) (fogoh)(x) = (fog)(x² + 3x - 2) (fogoh)(x) = 2(x² + 3x - 2) + 8 (fogoh)(x) = 2x² + 6x - 4 + 8 (fogoh)(x) = 2x² + 6x + 4 (fogoh)(-2) = 2(-2)² + 6(-2) + 4 (fogoh)(-2) = 2(4) - 12 + 4 (fogoh)(-2) = 8 - 12 + 4 (fogoh)(-2) = 0 Jadi, (fogoh)(-2) = 0.