di ketahui:f(x)=x³–2x²+4x-2 g(x)=x²+x-6 h(x)=x+3 tentukan (f+g)(x),(f+g)(x),(g×h)(x),(g/h)(x)​

Jawaban:Diketahui:f(x) = x³ – 2x² + 4x – 2g(x) = x² + x – 6h(x) = x + 3---1. (f + g)(x) = f(x) + g(x)= (x³ – 2x² + 4x – 2) + (x² + x – 6)= x³ + (-2x² + x²) + (4x + x) + (-2 – 6)= x³ – x² + 5x – 8---2. (f – g)(x) = f(x) – g(x)= (x³ – 2x² + 4x – 2) – (x² + x – 6)= x³ – 2x² + 4x – 2 – x² – x + 6= x³ – 3x² + 3x + 4---3. (g × h)(x) = g(x) × h(x)= (x² + x – 6)(x + 3)= x²(x + 3) + x(x + 3) – 6(x + 3)= x³ + 3x² + x² + 3x – 6x – 18= x³ + 4x² – 3x – 18---4. (g / h)(x) = g(x) ÷ h(x)= (x² + x – 6) ÷ (x + 3)Faktorkan pembilang:x² + x – 6 = (x + 3)(x – 2)Jadi:(g / h)(x) = (x + 3)(x – 2) ÷ (x + 3)= x – 2 (dengan syarat x ≠ -3 agar tidak membagi 0)---Jadi, hasilnya:(f + g)(x) = x³ – x² + 5x – 8(f – g)(x) = x³ – 3x² + 3x + 4(g × h)(x) = x³ + 4x² – 3x – 18(g / h)(x) = x – 2, x ≠ -3

Answered by dorotheaday7 | 2025-08-11