Verify inverse by composition

What you'll learn

1. State the formal definition of inverse functions using composition: f and g are inverses if f(g(x)) = x AND g(f(x)) = x
2. Verify an inverse relationship by computing both compositions symbolically and showing each simplifies to x
3. Explain why BOTH compositions must be checked, not just one
4. Use composition verification to catch errors in inverse-finding procedures
5. Verify inverse relationships numerically by evaluating f(g(a)) and g(f(a)) at several values
6. Apply the composition test to non-obvious pairs, including functions that might "look like" inverses but aren't

Prerequisites

• Compose functions
• Solve for inverse function