Mathematics · Polynomials and Functions

Let f, g : R → R be defined as: f(x) = a1 + a2x + a3x2 + a4x3 + a5x4 g(x) = b1 + b2x + b3x2 + b4x3 + b5x4 Define a function h : R → R such that h(x) = f(x + 2) + g(x - 1). Given that f(x + 1) = g(x - 1) for all x ∈ R, find the coefficient of x3 in h(x).