How to compute the inverse

Computing the inverse of a bijective function is a three-step procedure: write $y=f(x)$, isolate $x$, and swap the names of the variables.

Example — How to compute the inverse

Let $f(x) = 2x+3$, bijective from $\mathbb{R}$ to $\mathbb{R}$. To find $f^{-1}$:

1. Write $y = 2x+3$.
2. Isolate $x$: $x = \tfrac{y-3}{2}$.
3. Swap the names of the variables (convention: the independent variable of a function is always called $x$): $f^{-1}(x) = \tfrac{x-3}{2}$.

Links

Topics: Functions and properties
Concepts: Inverse function
Functions: Straight line
Skills: Solving equations · Using formulae