Mathematics · Grades 8–11
Inverse linear functions
Undo addition first, then undo multiplication.
The key idea
Undo addition first, then undo multiplication.
f⁻¹(y) = (y − b)/a, a ≠ 0
Worked examples
f(x) = 6x + (15). Find f⁻¹(-9).
(-9 − (15)) ÷ 6 = -4
-4
f(x) = 5x + (25). Find f⁻¹(135).
(135 − (25)) ÷ 5 = 22
22
Try it yourself
f(x) = 4x + (5). Find f⁻¹(1).
f(x) = 2x + (-12). Find f⁻¹(-34).
Check your understanding
Answers and marking notes
- -1
(1 − (5)) ÷ 4 = -1
- -11
(-34 − (-12)) ÷ 2 = -11
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.