Question

1. A binary operation * is defined on the set of real numbers, R, by x*y = 2x+2y-xy/5. Find: (a) the inverse of x under *; (b) the truth set when m*7 = -2*m.

Accepted Answer

(a) We need e such that x*e=x: 2x+2e-xe/5=x, so e(2-x/5)=-x, giving e=x/(x-10). This shows the identity element would depend on x, which is not allowed for a true identity element — so there is NO inverse element under this operation.
(b) m*7 = 2m+14-7m/5; -2*m = -4+2m-(-2m/5)=-4+2m+2m/5. Setting them equal and solving: 2m+14-7m/5 = -4+2m+2m/5 → 18 = 9m/5 → m = 10. Truth set = {10}.

WAEC Further Mathematics 2025 Theory — Question 1

Sign up free to unlock