Find the algebraic inverse of linear and rational functions to reverse their operations.
Inputs
Inverse Function
\frac{x - 4}{2}Inverse
f⁻¹(x)
\frac{x - 4}{2}
Steps
1Write as y = 2x + 4.
2Swap variables: x = 2y + 4.
3Subtract 4: x - 4 = 2y.
4Divide by 2: y = \frac{x - 4}{2}.
About this calculator
Concept
An inverse function undoes what the original function did. If $f(x)$ represents encrypting a message, $f^{-1}(x)$ represents decrypting it. Graphically, they are mirror images across the line $y=x$.
💡
Pro Tips
Switch $x$ and $y$ in the equation, then solve for the new $y$.
Only one-to-one functions have true inverse functions.
The domain of the function becomes the range of its inverse.
!
Fun Facts
"The notation $f^{-1}$ was introduced by John Herschel in 1813."
"Inverses are crucial in solving equations (e.g., using logarithms to solve exponentials)."
