Inverse Function Calculator
Compute the inverse of f(x) = ax + b and solve for the input that gives a chosen output.
Table of Contents
How to Use
- Enter the slope a (non-zero)
- Enter the intercept b
- Set the output value y you want to invert
- Calculate to see the inverse expression and solved x
Inverse of a linear function
For f(x) = ax + b with a ≠ 0, solve y = ax + b for x to get f⁻¹(y) = (y - b) / a. The inverse is also linear with slope 1/a.
Because a is non-zero, f is one-to-one and has domain and range over all real numbers.
Using the calculated inverse
- Plug the inverse into compositions to check f(f⁻¹(y)) = y
- Use the solved input x to translate between output values and their preimages
- Remember units: if y has units, the inverse preserves them through the division and subtraction steps
Frequently Asked Questions
- Why must a be non-zero?
- If a = 0, the function is constant and not one-to-one, so it has no inverse. Non-zero slope ensures each output corresponds to exactly one input.
- Is the inverse also linear?
- Yes. The inverse of ax + b is (y - b) / a, which is linear in y with slope 1/a and intercept -b/a.
- Can I use this for other function types?
- This calculator focuses on linear functions. For quadratics or rational functions, you need different algebra and may not get a single-valued inverse without restricting the domain.