The functions f and g are defined for x R by f: x x 1

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The functions f and g are defined for x ∈ R by f: x ↦ x² −1 g: x ↦ 3x + 4

a) Find and simplify expressions for fg(x) and gf(x).

b) Hence find the values of a for which
fg(a) = 4a + gf(a).

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