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Previous Year Question (PYQs)

If $S$ is the set of all real numbers except $-1$ and $*$ is defined by $a * b = a + b + ab$, then the inverse of $2 * 3$ is





Solution

First compute:

$2 * 3 = 2 + 3 + (2)(3) = 11$

Inverse element $x$ satisfies:

$11 * x = 0$ (identity element is $0$)

$11 + x + 11x = 0$

$x(12) = -11$

$x = -\frac{11}{12}$


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