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Question
If f: R → R is defined by f(x) = x2 − 3x + 2, find f(f(x)).
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Solution
f(x) = x2 - 3x + 2
∴ f (f (x)) = f (y) where
y = x2 − 3x + 2
= y2 − 3x + 2
= (x2 − 3x + 2)2 − 3(x2 = 3x + 2) + 2
= x4 + 9x2 + 4 − 6x3 + 4x2 − 12x − 3x2 + 9x − 6 + 2
= x4 − 6x3 + 10x2 − 3x
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