Inverse Function Calculator
Enter a linear function's slope and intercept below to instantly find its inverse.
For f(x) = mx + b
Finding an Inverse Function
For f(x) = mx + b, the inverse is f⁻¹(x) = (x − b) / m — swap x and y, then solve for the new y.
Worked example
Find the inverse of f(x) = 2x + 3.
y = 2x + 3 → x = 2y + 3 → y = (x − 3) / 2
f⁻¹(x) = 0.5x − 1.5
A second example
Find the inverse of f(x) = −3x + 6.
y = −3x + 6 → x = −3y + 6 → y = (6 − x) / 3
f⁻¹(x) = 2 − x/3
Keep going
- An inverse function swaps x and y in a linear equation; the slope-intercept calculator builds the original equation that this one is inverting. Slope-Intercept Form Calculator
Frequently Asked Questions
What is an inverse function?
An inverse function undoes what the original function does. If f(x) turns 3 into 7, then f⁻¹(x) turns 7 back into 3.
How do you find the inverse of a linear function?
Swap x and y in y = mx + b, giving x = my + b, then solve for y: y = (x − b) / m.
Why does this calculator only handle linear functions?
Linear functions always have a clean, closed-form inverse. Many other function types (like most quadratics) aren't one-to-one over their whole domain, so a general inverse doesn't exist without restricting the domain first — a more involved case-by-case problem than a single calculator can handle generically.
Does f⁻¹(x) mean 1 divided by f(x)?
No — this is a very common mix-up. f⁻¹(x) is function notation for "the inverse function," not an exponent applied to f(x). The reciprocal of a function is written 1/f(x), which is a completely different thing.
What does the graph of an inverse function look like?
It's the mirror image of the original function's graph, reflected across the line y = x. Every point (a, b) on f(x) corresponds to a point (b, a) on f⁻¹(x).
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