Rational, Radical, and Function Operations
Aligned to F-BF.B.4 — Common Core State Standards for Mathematics.
What this lesson teaches
An inverse function undoes what the original function did, swapping inputs and outputs. If a function adds 3, its inverse subtracts 3. You can also combine functions by composing them, where the output of one becomes the input of the next.
Worked example
If f(x) = x + 3, then to undo it the inverse is f-inverse(x) = x - 3. Check: f(2) = 5, and the inverse takes 5 back to 2.
Practice questions
- Find the inverse of f(x) = x - 7.
- Find the inverse of f(x) = 2x.
- If f undoes g, what is f(g(4))?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Operaciones con Funciones Racionales, Radicales e Inversas
Una función inversa deshace lo que hizo la función original, intercambiando entradas y salidas. Si una función suma 3, su inversa resta 3. También puedes combinar funciones al componerlas, donde la salida de una se convierte en la entrada de la siguiente.
Ejemplo: Si f(x) = x + 3, entonces para deshacerla la inversa es f-inversa(x) = x - 3. Comprobación: f(2) = 5, y la inversa lleva 5 de regreso a 2.
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