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(i) *:R x R → Ris given by a * b = 3a2 – b 

Find the value of 2 * 3. Is ‘*’ commutative? Justify your answer.

(ii) ƒ :R → R is defined by ƒ(x) = x2 – 3x + 2 Find f of (x) and f of

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(i) 2 * 3 = 3 x 22 - 3 = 12 - 3 = 9

Given ; a*b = 3a2 - b

b*a = 3b2 - a ≠ a*b

Hence not commutative.

(ii) f of (x) = f (f(x)) = f (x2 -3x +2)

=(x-3x + 2)2 - 3 (x2 - 3x + 2)

= x4 + 9x2 + 4 - 6x3 + 4x2 - 12x - 3x2 + 9x - 6 +2

= x4 - 6x3 + 10x2 - 3x

f of (1) = 1 - 6 + 10 - 3 = 2

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