The inverse function f⁻¹ reverses f: if f(3) = 7, then f⁻¹(7) = 3. To find it, write y = f(x), swap x and y, then make y the subject.
For f(x) = (x − 3)/3: write x = (y − 3)/3, so 3x = y − 3 and y = 3x + 3. So f⁻¹(x) = 3x + 3, and f⁻¹(7) = 24. The graph of y = f⁻¹(x) is the reflection of y = f(x) in the line y = x.
Worked example
f(x) = 2x + 2. Find f⁻¹(x).
- Swap: x = 2y + 2.
- x − 2 = 2y, so y = (x − 2)/2.
Answer:f⁻¹(x) = (x − 2)/2
Key words
- inverse
- the function that undoes f
- f⁻¹
- the notation for the inverse
- reflection in y = x
- how the inverse graph is drawn
Practise this
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Common Core-referenced: HSF-BF.B.4a