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

Assessment: JAMB UTME - Mathematics - 2024 Subject: General Mathematics

Question 1 Report

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.

0, 2

1, 2

0, 1

2, 2

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.

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Binary Operations

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

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