Answer:
(F ° G)(x) = x⁶ + 16x⁴ + 84x² + 147
Step-by-step explanation:
Assuming that (FG)(x) = F ° G (x) = F(G(x))
(F ° G) (x) = f(g(x)) = (x² + 5)³ + (x² + 5)² – (x² + 5) + 2
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(a + b)³ = a³ + 3a²b + 3ab² + b³
(a + b)² = a² + 2ab + b²
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(F ° G) (x) =
((x²)³ + 3(x²)²(5) + 3(x²)(5)² + (5)³) + ((x²)² + 2(x²)(5) + (5)²) + (-x² – 5) + 2 =
(x⁶ + 15x⁴ + 75x² + 125) + (x⁴ + 10x² + 25) + (-x² – 5) + (2) =
x⁶ + 16x⁴ + 84x² + 147
