Inverse Function Calculator
How It Works
This inverse function calculator uses established formulas to provide accurate results.
The basic rule:
- To find f⁻¹: swap x and y, solve for y
- f(x) = ax + b → f⁻¹(x) = (x - b)/a
- Verification: f(f⁻¹(x)) = x
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is an inverse function?
An inverse function f⁻¹ reverses the effect of f. If f(3) = 7, then f⁻¹(7) = 3. Applying f and then f⁻¹ (or vice versa) returns you to the original input.
How do I find an inverse function?
Replace f(x) with y, swap x and y, then solve for y. For f(x) = 3x - 7: write y = 3x - 7, swap to get x = 3y - 7, solve for y = (x + 7)/3.
Do all functions have inverses?
No. A function must be one-to-one (pass the horizontal line test) to have an inverse. If any horizontal line crosses the graph more than once, the function does not have an inverse without restricting the domain.
How is the inverse related to the graph?
The graph of f⁻¹ is the reflection of f across the line y = x. Every point (a, b) on f becomes (b, a) on f⁻¹.