Inverse Functions
Aligned to F-BF.B.4 — Common Core State Standards for Mathematics.
What this lesson teaches
An inverse function undoes another: swap x and y, then solve for y. Two functions f and g are inverses exactly when f(g(x)) = x and g(f(x)) = x.
Worked example
Let f(x) = 2x + 6. Swap to get x = 2y + 6, so y = (x − 6)/2. Check: f((x − 6)/2) = 2 × (x − 6)/2 + 6 = (x − 6) + 6 = x, so it is verified.
Practice questions
- Find the inverse of f(x) = x − 7.
- Find the inverse of f(x) = 3x.
- Verify that f(x) = x^3 and g(x) = √[3]{x} are inverses by composition.
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
Funciones inversas
Una función inversa deshace a otra: intercambia x y y, luego despeja y. Dos funciones f y g son inversas exactamente cuando f(g(x)) = x y g(f(x)) = x.
Ejemplo: Sea f(x) = 2x + 6. Intercambia para obtener x = 2y + 6, así que y = (x − 6)/2. Comprueba: f((x − 6)/2) = 2 × (x − 6)/2 + 6 = (x − 6) + 6 = x, entonces queda verificado.
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