The function $f(x) = 2x + 1$ on $\reals$ under composition of functions
Terms
| Term | This example | Why |
|---|---|---|
| inverse element | $f^{-1}(x) = \frac{x - 1}{2}$ | For composition of functions $\reals \to \reals$, the identity element is the identity function $x \mapsto x$, so the inverse element of $f(x) = 2x + 1$ is the inverse function $f^{-1}(x) = \frac{x - 1}{2}$, because $f(f^{-1}(x)) = f^{-1}(f(x)) = x$ for all $x$. |