Additional Mathematics – Functions | e-Consult

The absolute value function maps both a positive number and its negative counterpart to the same non‑negative result (e.g., \(|3| = |-3| = 3\)). This duplication means the function is not one‑to‑one; a horizontal line at any positive \(y\) intersects the graph at two points. Consequently, no inverse function exists on the entire real line unless the domain is restricted to \(x\ge 0\) or \(x\le 0\).