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Learning Goal
Part of: Build new functions from existing functions — 3 of 7 cluster items
Solve for inverse function
HSF.BF.B.4.a
**HSF.BF.B.4.a**: 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. For example, f(x) = 2x³ or f(x) = (x+1)/(x-1) for x ≠ 1.
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HSF.BF.B.4.a: 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. For example, f(x) = 2x³ or f(x) = (x+1)/(x-1) for x ≠ 1.
What you'll learn
- Solve f(x) = c for x, where f is a simple invertible function, by algebraically isolating x
- Use the "swap x and y, then solve for y" method to find the inverse function algebraically
- Find inverse functions for linear functions (f(x) = ax + b)
- Find inverse functions for simple power functions (f(x) = x³, f(x) = x² with restricted domain)
- Find inverse functions for simple rational functions (f(x) = (x+a)/(x+b))
- Verify the inverse by checking f(f⁻¹(x)) = x
Prerequisites
Slides
Interactive presentations perfect for visual learners • Interactive presentation
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Exercises
Practice problems to build fluency and understanding • 1 exercises