A binary operation * is defined on a set of real numbers by x*y = xy for all values of x and y, if x * 2 = x, find the possible values of x.
Answer Details
The problem defines a binary operation "*" on real numbers by the expression \(x * y = x^y\). You are given the condition that \(x * 2 = x\). In mathematical terms, this translates to:
\(x^2 = x\)
To solve for the possible values of \(x\), we can rewrite the equation as:
\(x^2 - x = 0\)
We can factor the left side of the equation:
\(x(x - 1) = 0\)
This equation implies that either \(x = 0\) or \(x - 1 = 0\). Solving these gives us:
\(x = 0\)
\(x = 1\)
Therefore, the possible values of \(x\) are 0 and 1. This solution matches the option of 0, 1.