Relate a function's domain to its graph and to the real-world quantities it describes.
Identify an input outside the domain
Problem
For \(f(x)=1/(x-4)\), diagnose proposed input \(x=4\).
Big Picture
What this problem is really about
To diagnose a proposed input, test it against the operation that can make the rule undefined. We’ll write the nonzero-denominator condition, substitute the proposed value into that denominator, and interpret the resulting quotient. This distinguishes an excluded input from an input whose output is zero and avoids treating infinity as an ordinary function value.
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