The binary operation * is defined on the set of R, of real numbers by \(x * y = 3x + 3y - xy, \forall x, y \in R\). Determine, in terms of x, the identity element of the operation.
A. \(\frac{2x}{x - 3}, x \neq 3\) B. \(\frac{2x}{x + 3}, x \neq -3\) C. \(\frac{3x}{x - 3}, x \neq 3\) D. \(\frac{3x}{x + 3}, x \neq -3\)
Correct Answer: A
Explanation
From the rules of binary operation, \(x * e = x\) \(\implies x * e = 3x + 3e - xe = x\) \(3e - xe = x - 3x = -2x\) \(e = \frac{2x}{x - 3}, x \neq 3\)
