Find 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

Question

A. p
B. p -1
C. p/(p-1)
D. p/(p+1)

Answer 1

To find the inverse of p under the binary operation *, we need to find a number x such that p * x = x * p = 0, where 0 is the identity element.

Let's assume the inverse of p is x. Then we have: p * x = p + x - px = 0.

We can rearrange this equation to solve for x:
p + x - px = 0
x - px = -p
x(1 - p) = -p
x = -p / (1 - p)

Therefore, the inverse of p is x = -p / (1 - p).

The correct answer is D. p / (p + 1).