JAMB 1993 · UME · Q24✱✱

Binary operations

A binary operation $*$ is defined on the set of real numbers by $x * y = x^y$ for all real values of $x$ and $y$ . If $x * 2 = x$ , find the possible values of $x$ .

Worked solution (try it first)

By the definition, $x * 2 = x^2$ , so the equation is $x^2 = x$ .
Bring everything to one side and factorise: $x^2 - x = x(x - 1) = 0$ .
So $x = 0$ or $x = 1$ , option A.

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