2000
Mathematics
67ca00ce0c643c71d77dee1f
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
A.
p
B.
p -1
C.
p/(p-1)
D.
p/(p+1)
Correct Answer: p/(p-1)
Explanation
If P-1 is the inverse of P and O is the identity, Then P-1 * P = P * P-1 = 0 i.e. P-1 + P - P-1.P = 0 P-1 - P-1.P = -P P-1(1 - P) = -P P-1 = -P/(P-1) = P/(P-1)
If P-1 is the inverse of P and O is the identity, Then P-1 * P = P * P-1 = 0 i.e. P-1 + P - P-1.P = 0 P-1 - P-1.P = -P P-1(1 - P) = -P P-1 = -P/(P-1) = P/(P-1)THIS WEEK's
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