A binary operation * is defined on the set of real numbers, R, by \(x
FURTHER MATHEMATICS
WAEC 2013
A binary operation * is defined on the set of real numbers, R, by \(x * y= x + y - xy\). If the identity element under the operation * is 0, find the inverse of \(x \in R\).< p>
- A.\(\frac{-x}{1 - x}, x \neq 1\)
- B.\(\frac{1}{1 - x}, x \neq 1\)
- C.\(\frac{-1}{1 - x}, x \neq 1\)
- D.\(\frac{x}{1 - x}, x \neq 1\)
Correct Answer: A.\(\frac{-x}{1 - x}, x \neq 1\)
Explanation
\(x * y = x + y - xy\)
Let \(x^{-1}\) be the inverse of x, so that
\(x * x^{-1} = x + x^{-1} - x(x^{-1}) = 0\)
\(x + x^{-1} - x(x^{-1}) = 0 \implies x(x^{-1}) - x^{-1} = x\)
\(x^{-1}(x - 1) = x \implies x^{-1} = \frac{x}{x - 1}\)
= \(\frac{x}{-(1 - x)} = \frac{-x}{1 - x}, x \neq 1\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *