Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.
Prove or disprove oddness using f(-x) and -f(x)
Problem
Test \(f(x)~=~x^3~-~5x\) for oddness. Address domain symmetry, simplify \(f(-x)\) and \(-f(x)\), compare them, and state the conclusion.
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What this problem is really about
Testing oddness requires a symmetric domain and a precise comparison between two independently formed expressions. Compute f of negative x by replacing every input, then compute negative f of x by distributing an outside negative across the entire original output. Only after both lines are simplified should their equality be judged.
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