CCSS.Math.Content.HSF-BF.B.4a
The standard
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.
Common Core State Standards for Mathematics · Build new functions from existing functions
What this standard means
Students need to undo a function step by step. They solve f(x) = c, then swap the role of the input and output to write the inverse rule. They should handle linear, simple power, root, and basic rational functions, while paying attention to restrictions.
Mastery looks like writing a correct inverse and checking it by composing or testing ordered pairs. Students often get stuck treating inverse as “flip the fraction,” forgetting domain limits, or losing plus and minus signs when undoing squares or square roots.
Ways to teach it
- Hands-on activity: Give pairs function cards and output cards, then have them build inverse steps with sticky notes in reverse order.
- Writing prompt: Explain how solving f(x)=c helps you write f inverse, using f(x)=3x-5 as your example.
- Quick assessment: Exit ticket with f(x)=(x+2)/3 and g(x)=x^2, x≥0, asking for each inverse and one check.
- Real-world connection: Use Celsius to Fahrenheit conversion, then ask students to write and use the inverse to recover Celsius from Fahrenheit.
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Related standards
- CCSS.Math.Content.HSF-BF.B.4
Find inverse functions.
- CCSS.Math.Content.HSF-TF.B.7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms...
- 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.