Exam Strategy

Readiness Check

You are ready when you can:

• Decide invertibility on a stated domain.
• Reverse pairs and swap domain/range.
• Reflect a graph over $y=x$.
• Find $f^{-1}$ algebraically and verify with composition.
• Apply contextual limits to the inverse.

On the AP Exam

• MCQ: invertibility, table/graph inverses, algebraic form, domain of $f^{-1}$.
• FRQ: restrict domain, find inverse, verify, interpret in context.
• Skills: 1.A solve analytically; related representation skills from Unit 2.

Tactics

1. Check unique output $\leftrightarrow$ unique input on the given domain. 2. Table: swap columns; graph: reflect over $y=x$. 3. Algebra: $y=f(x)$, swap, solve for $y$, rename as $f^{-1}(x)$. 4. Verify: $f(f^{-1}(c))=c$ and $f^{-1}(f(c))=c$ for a test value. 5. State Dom$(f^{-1})=$ Range$(f)$ on the invertible piece.

Common Traps

• Reciprocal confusion.
• Full-domain inverse for non-one-to-one functions.
• Wrong domain for $f^{-1}$.
• Skipping verification by composition.

Quick Checklist

• [ ] Invertible on stated domain?
• [ ] Pairs / graph / algebra consistent?
• [ ] Domain and range of $f^{-1}$ stated?
• [ ] Context limits noted if given?