Inverse Function Calculator (Linear)
Find the inverse of y = mx+b.
Enter your values
Enter the slope m you are working with.
Enter the intercept b you are working with.
Enter the test x for f^-1(x) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- f^-1(x) formula
- f^-1(x) = (x - 3) / 2
- f^-1(7)
- 2
- Check: f(f^-1(x))
- 7
Quick answer
The inverse of y = mx+b is x = (y-b)/m, i.e. f^-1(x) = (x-b)/m.
f^-1(x) = (x-b)/m
At a glance
| What it does | Find the inverse of y = mx+b. |
|---|---|
| Category | Math |
| Inputs needed | Slope m, Intercept b, Test x for f^-1(x) |
| Main output | f^-1(x) formula |
| Formula | f^-1(x) = (x-b)/m |
| Cost | Free — no sign-up, no download |
How to use the Inverse Function Calculator (Linear)
- 1Enter the slope m and intercept b of f(x)=mx+b.
- 2The tool swaps x and y and solves for the new y to get the inverse.
- 3Optionally test a value to confirm f(f^-1(x)) returns the original input.
Inputs explained
- Slope m
- Enter the slope m you are working with.
- Intercept b
- Enter the intercept b you are working with.
- Test x for f^-1(x)
- Enter the test x for f^-1(x) you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Slope m2
- Intercept b3
- Test x for f^-1(x)7
Results
- f^-1(x) formulaf^-1(x) = (x - 3) / 2
- f^-1(7)2
- Check: f(f^-1(x))7
Frequently asked questions
Does every function have an inverse?
Only one-to-one functions do; linear functions with m≠0 always qualify.
What if m=0?
The function is constant and has no inverse.
What do I need to enter into the Inverse Function Calculator (Linear)?
Just 3 values: slope m, intercept b, test x for f^-1(x). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Inverse Function Calculator (Linear) work out the answer?
The inverse of y = mx+b is x = (y-b)/m, i.e. f^-1(x) = (x-b)/m. It applies the formula f^-1(x) = (x-b)/m and shows the working so you can check each step by hand.
Is the Inverse Function Calculator (Linear) free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.