A binary operation \(\oplus\) om real numbers is defined by x \(\oplus\) y = xy...

JAMB 2011

A binary operation \(\oplus\) om real numbers is defined by x \(\oplus\) y = xy + x + y for two real numbers x and y. Find the value of 3 \(\oplus\) - \(\frac{2}{3}\).

A. - \(\frac{1}{2}\)
B. \(\frac{1}{3}\)
C. -1
D. 2

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Correct Answer: Option B

Explanation

N + Y = XY + X + Y

3 + -\(\frac{2}{3}\) = 3(- \(\frac{2}{3}\)) + 3 + (- \(\frac{2}{3}\))

= -2 + 3 -\(\frac{2}{3}\)

= \(\frac{1 - 2}{1 - 3}\)

= \(\frac{1}{3}\)

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