Question 14
Binary OperationsFind the inverse of p under the binary operation * defined by p*q = p + q − pq, where p and q are real numbers and zero is the identity.
- A.p
- B.p − 1
- C.p/(p − 1)
- D.p/(p + 1)
Show the answer and explanation
Answer: C (p/(p − 1))
Explanation
The inverse q satisfies p*q = 0, so p + q − pq = 0. Then q(1 − p) = −p, so q = p/(p − 1).