Verify inverse by composition
Start lessonBegins with Verifying inverses by composition · Slides
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
HSF.BF.B.4.b
**HSF.BF.B.4.b**: (+) Verify by composition that one function is the inverse of another.
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HSF.BF.B.4.b: (+) Verify by composition that one function is the inverse of another.
What you'll learn
- State the formal definition of inverse functions using composition: f and g are inverses if f(g(x)) = x AND g(f(x)) = x
- Verify an inverse relationship by computing both compositions symbolically and showing each simplifies to x
- Explain why BOTH compositions must be checked, not just one
- Use composition verification to catch errors in inverse-finding procedures
- Verify inverse relationships numerically by evaluating f(g(a)) and g(f(a)) at several values
- Apply the composition test to non-obvious pairs, including functions that might "look like" inverses but aren't
Review first:
Slides
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Verifying inverses by composition
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