CCSS.Math.Content.HSF-BF.B.4
The standard
Find inverse functions.
Common Core State Standards for Mathematics
What this standard means
Students need to undo a function and write the rule that reverses it. They should switch x and y, solve for y, and use correct notation. They also need to check by composing the two functions and getting x back both ways.
Mastery means students can find inverses for linear, quadratic with a restricted domain, radical, exponential, and rational functions when appropriate. They know not every relation has an inverse function. Common trouble spots are solving algebra steps, forgetting domain restrictions, and thinking the inverse of f(x) is always 1/f(x).
Ways to teach it
- Hands-on activity: Give students function machines made from index cards, then have them build the reverse machine and write both rules.
- Prompt: Explain why f inverse does not mean the reciprocal of f, using one example and one non-example.
- Quick assessment: Give three functions and ask students to find each inverse, state any domain restriction, and verify one with composition.
- Real-world connection: Use Celsius and Fahrenheit conversion formulas, then have students derive the reverse formula and test it with actual temperatures.
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Related standards
- CCSS.Math.Content.HSF-BF.B.4a
Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
- CCSS.Math.Content.HSF-BF.B.4c
(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
- CCSS.Math.Content.HSF-BF.B.4b
(+) Verify by composition that one function is the inverse of another.
- CCSS.Math.Content.HSF-BF.B.4d
(+) Produce an invertible function from a non-invertible function by restricting the domain.