Relate a function's domain to its graph and to the real-world quantities it describes.
Find the mathematical domain of a rational function
Problem
Determine the mathematical domain of \(f(x)=1/(x-4)\).
Big Picture
What this problem is really about
A rational expression accepts every real input except those that make a denominator zero. We’ll isolate the denominator, solve the equation that makes it vanish, and verify the restriction by substitution. Since no radical or other restricting operation appears, that check identifies the single hole in an otherwise all-real mathematical domain.
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