To assess whether a function is injective (also referred to as one-to-one), it's essential to verify that each input correlates to a distinct output. If there's even a single instance where two diverse inputs yield the same output, the function fails to be injective. A convenient way to visually confirm this is by examining a graph; if any horizontal line intersects the curve more than once, the function is not one-to-one.
Topic | Problem | Solution |
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None | Determine if the relation \(f(x) = 3x^2 - 2x + 1\… | Step 1: Assume that \(f(a) = f(b)\) for some \(a, b\) in the domain of \(f\). We have \(3a^2 - 2a +… |