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f Versus f(x) — What Does Each Symbol Represent?
publish date: 2026/05/23 18:30:33.480006 UTC
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Consider the diagram below — a function acts like a machine: you feed in an input and get an output.
In the notation \(f: A \to B\), the single letter \(f\) represents:
Correct Answer
The rule of correspondence that converts each element of A into an element of B
Explanation
\(f\) names the rule (the machine itself) — it may be a formula, a method, or a statement. The symbol \(f(x)\) is the output produced when that rule is applied to the specific input \(x\). These two symbols must never be confused: \(f\) is the machine; \(f(x)\) is what the machine produces.
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012