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: Option 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)