A binary operation * is defined on a set of real numbers by x*y = x\(^y\) for all values of x and y, if x * 2 = x, find the possible values of x.
Given the operation defined by \( x * y = x^y \),
\[x * 2 = x \implies x^2 = x\]
Rearranging gives: \[x^2 - x = 0 \implies x(x - 1) = 0\]
Thus, the possible values of \( x \) are: \[\boxed{0 \text{ and } 1}\]
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