Inverse Function Solver

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Calculate the algebraic inverse of linear functions and explore symmetry across y = x.

Function Coefficients

f(x) = 2x + 3

Slope (a)

Y-Intercept (b)

Inverse Result

0.50x - 1.50

f⁻¹(x) =

The reflection of the function across the line y = x

Inverse Slope0.5000

Inverse Intercept-1.5000

About this calculator

What is an Inverse Function?

An inverse function 'undoes' the operation of the original function. If f(x) takes x to y, then the inverse f⁻¹(y) takes y back to x. Graphically, the inverse of a function is its reflection across the line y = x. Only 'one-to-one' functions have an inverse that is also a function.

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Pro Tips

Switching x and y: The algebraic method for finding an inverse is to replace f(x) with y, swap x and y, and solve for the new y.
Domain and Range: The domain of a function becomes the range of its inverse, and vice versa.
Horizontal Line Test: Use this on the original graph to see if its inverse will actually be a function.

Fun Facts

"The 'ln' (natural log) function is the inverse of the 'eˣ' (exponential) function."
"Inverse trigonometry (like arcsin) is used to find angles when you only know side ratios."
"Not every function has an inverse; for example, f(x) = x² only has an inverse if we restrict the domain to x ≥ 0."

Formula: For f(x) = ax + b, the inverse is f⁻¹(x) = (x - b) / a