Function Inverse Calculator (Linear)

This function inverse calculator finds the inverse of a linear function written as f of x equals mx plus b. Enter the slope m and the intercept b, and the calculator gives the inverse function, which undoes what f does, plus its value at a point you choose and a check. To invert a linear function you swap the roles of input and output and solve for the new output: subtract the intercept then divide by the slope. A linear function has an inverse exactly when its slope is not zero, so that different inputs always give different outputs. The method, a worked example and the assumptions are below.

Slope m

Intercept b

Evaluate inverse at x

Inverse at x

Check f(inverse)

The formula

For f(x) = mx + b, the inverse is f inverse of x = (x minus b) / m, valid when m is not zero. The graph of the inverse is the reflection of f across the line y = x.

Worked example

For f(x) = 2x + 3, the inverse is (x minus 3) / 2. Evaluating at x = 7 gives (7 minus 3)/2 = 2, and f(2) = 7, which checks out. Enter 2, 3, 7 to confirm.

Frequently asked questions

How do I find the inverse of a linear function?

Swap x and y, then solve for y. For mx + b this gives (x minus b) / m.

When does a linear function have an inverse?

Whenever the slope m is non-zero, so the function is one-to-one. A horizontal line (m = 0) has no inverse.

What does the inverse do?

It reverses the function: if f sends a to b, the inverse sends b back to a.

Who this calculator is for

This calculator is for algebra students and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid numbers.
The standard method is applied.
Results are rounded for display.

Formula and sources

Related calculators

Quadratic Formula Calculator: solve a quadratic.
Scientific Calculator: general maths.
Matrix Calculator: matrix operations.

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