Solve equations of the form f(x)=g(x) approximately by finding graph/table intersections.
Use sign changes to bracket an approximate solution
Problem
Use the table of \(f(x)~-~g(x)\) values below to narrow the interval where \(f(x)~=~g(x)\). Assume \(f(x)~-~g(x)\) changes continuously between listed \(x\)-values.
Equality occurs where the difference between the functions is zero. We’ll scan the table for adjacent entries with opposite signs and use the closest such pair as the narrowest supported bracket. Because the prompt guarantees continuity between listed inputs, moving from negative to positive forces a zero inside that interval, while neither endpoint counts as exact unless its displayed difference is zero.
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