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Question
If f: R → R is defined by f(x) = x2 – 3x + 2, write f(f (x))
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Solution
Given that f(x)= x2 – 3x + 2
f(f(x) = f(x2 – 3x + 2)
= (x2 – 3x + 2)2 – 3(x2 – 3x + 2) + 2
= x4 + 9x2 + 4 – 6x3 – 12x + 4x2 – 3x2 + 9x – 6 + 2
= x4 + 10x2 – 6x3 – 3x
f(f(x)) = x4 – 6x3 + 10x2 – 3x
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