Function structure and algebraic proofs

Develop algebraic proof skills for precalculus functions through parity identities, even–odd decomposition and parameter-dependent invertibility. This optional extension builds on even and odd functions, inverse functions and counterexamples, moving from short substitution arguments to proofs of uniqueness and injectivity.

Practice single-select and select-all questions that require you to track symmetric domains, exceptional parameter values and inverse ranges. Worked explanations show why each claim follows and where tempting shortcuts fail. Solve the proof steps on paper before consulting the options; the saved course-reuse prompts support later written proof practice.