Relate a function's domain to its equation, graph, and context, especially when model choice matters.
Find the domain of a rational function by excluding denominator zeros
Problem
What is the domain of \(f(x)=1/(x-4)\)?
Big Picture
What this problem is really about
Domain questions for rational expressions begin in the denominator, not the numerator. Find every input that makes the denominator zero, exclude those values, and keep all remaining real inputs. A canceled factor would still preserve an original restriction, so simplification never grants permission to forget where the starting expression was undefined.
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