Q3 of 107 Page 29

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

It is given that f : R → R is defined by 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 - 6x3 + 10x2 - 3x


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