Function Inverse Calculator (Linear)

This function inverse calculator finds the inverse of a linear function of the form f(x) = mx + b, the related function that reverses it and sends each output back to the input that produced it. You enter three numbers: the slope m, the intercept b, and a value of x at which to evaluate the inverse. The calculator returns the inverse function itself, written as f-inverse(x) = (x - b)/m, the inverse evaluated at your chosen x, and a check that feeds that result back through the original f(x) to confirm it returns to x. To find a linear inverse by hand you swap input and output, then rearrange: subtract the intercept and divide by the slope. A linear function only has an inverse when its slope is not zero, because a horizontal line sends every input to the same output and cannot be reversed; enter m = 0 and the calculator will tell you no inverse exists. This tool suits algebra students checking homework, anyone verifying working by hand, and anyone wanting a fast, reliable answer without doing the algebra themselves. Try the defaults of m = 2 and b = 3 evaluated at x = 7 to match the worked example on the page, then swap in your own slope, intercept and x value to solve any linear inverse in seconds.

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Slope m

Intercept b

Evaluate inverse at x

f−1(x) = (x - 3) / 2

Inverse at x2

Check f(inverse)7

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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