Question:
if f;R....R and g : R....R defined by (x) =x^2 -3x 2.find the f(f(x).
Answer:
Given, f(x) = x2 - 3x + 2
Now, f(f(x)) = f(x2 - 3x + 2)
= (x2 - 3x + 2)2 - 3(x2 - 3x + 2) + 2
= (x2 - 3x + 2){x2 - 3x + 2 - 3} + 2
= (x2 - 3x + 2){x2 - 3x - 1} + 2
= x4 - 3x3 - x2 - 3x3 + 9x2 + 3x + 2x2 - 6x - 2 + 2
= x4 - 3x3 - x2 - 3x3 + 9x2 + 3x + 2x2 - 6x
= x4 - (3 + 3)x3 + (9 + 2 - 1)x2 + (3 - 6)x
= x4 - 6x3 + 10x2 - 3x
So, f(f(x)) = x4 - 6x3 + 10x2 - 3x
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