Grade 12 · Mathematics
Inverses
Why it matters
Reversing functions.
Advanced20m readingPrerequisite: Stretches
What is an inverse function?
Short answer
An inverse function reverses another function: if f maps x to y, its inverse f⁻¹ maps y back to x. You find it by swapping x and y and solving for y. A function has an inverse only if it is one-to-one (passes the horizontal line test), and the graph of f⁻¹ is the reflection of f across the line y = x.
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Frequently asked questions
- When does a function have an inverse?
- Only when it is one-to-one — each output comes from exactly one input, which it passes the horizontal line test.
- How are a function and its inverse related graphically?
- Their graphs are mirror images across the line y = x.