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Inverse Function Calculator

Online inverse function calculator: find the inverse of the linear y=ax+b, with the graph symmetric about y=x.

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f⁻¹(f(x))=x; symmetric about y=x
y=xff⁻¹
a≠0
y=ax+b

📖 Tutorial | Inverse Function

1. Definition
If y=f(x) is one-to-one, solve x=φ(y); φ is the inverse function f⁻¹, usually written y=f⁻¹(x).
2. Formula & Notation
fOriginal
f⁻¹Inverse
y=xAxis of symmetry
3. Properties & Laws
  • f⁻¹(f(x))=x;
  • Domain and range swap;
  • Symmetric about y=x;
  • Only one-to-one functions;
  • Inverse of ax+b is (x−b)/a.
4. Steps
  1. Enter a, b;
  2. Click "Find inverse";
  3. Or click "Load Example".
5. Worked Examples
Example: y=2x+1 gives x=(y−1)/2, hence y=(x−1)/2.
6. Common Pitfalls
Swap x and y after solving;
a≠0;
Non-one-to-one functions need a restricted interval.

❓ FAQ | Inverse Function

What is it?
It undoes the original.
How to find?
Solve for x, then swap.
Graph?
Symmetric about y=x.
Domain/range?
Swapped.
Which functions?
One-to-one (monotonic).
Reciprocal?
No, not 1/f.
Linear?
(x−b)/a.