Question:
If f: R → R is defined by f (x) = x2 – 3x + 2, write f (f (x)).
Solution:
Given, f (x) = x2 – 3x + 2
Then,
f (f (x)) = f (x2 – 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
Thus,
f (f (x)) = x4 – 6x3 + 10x2 – 3x
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