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If f : R → R is defined by f(x) = x² – 3x + 2, find f[f(x)].

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If f : R → R is defined by f(x) = x² – 3x + 2, find f[f(x)].

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f(x) = x² – 3x + 2

f[f(x)] = [f(x)]² – 3[f(x)] + 2

= (x² – 3x + 2)² – 3(x² -3x + 2) + 2

= (x4 + 9x² + 4 – 6x³ – 12x + 4x²) – 3x² + 9x – 6 + 2

= x4 – 6x³ + 10x² – 3x.

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