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WAEC Further Mathematics 2007 Question 10

Question 10

Binary Operations

The binary operation * is defined on the set R, of real numbers by x * y = 3x + 3y − xy for all x, y ∈ R. Determine, in terms of x, the identity element of the operation.

  1. A.2x/(x − 3), x ≠ 3
  2. B.2x/(x + 3), x ≠ −3
  3. C.3x/(x − 3), x ≠ 3
  4. D.3x/(x + 3), x ≠ −3
Show the answer and explanation

Answer: A (2x/(x − 3), x ≠ 3)

Explanation

The identity e satisfies x * e = x: 3x + 3e − xe = x, so e(3 − x) = −2x and e = 2x/(x − 3).