Let&nbsp;\(A\) be a fixed subset of \(\mathbb{R}\).
Define \(\mathrm{id}_A\) to be \[
\mathrm{id}_A(x) = x 
\] for all \(x \in A\).
We say that&nbsp;\(\mathrm{id}_A\) is the identity function on the set \(A\).
Intuitively, the identity function on a set&nbsp;\(A\) leaves every element of \(A\) untouched. Some books use the notation \(1_A\) to denote the identity function on the set&nbsp;\(A\).

Let \(A\) be a fixed subset of \(\mathbb{R}\).

Define \(\mathrm{id}_A\) to be 
\[
\mathrm{id}_A(x) = x 
\]
for all \(x \in A\).

We say that \(\mathrm{id}_A\) is the **identity function on the set** \(A\).

Intuitively, the identity function on a set \(A\) leaves every element of \(A\) untouched.  Some books use the notation \(1_A\) to denote the identity function on the set \(A\).

Functions

International Baccalaureate Higher Level Mathematics

Identity functions

Identity functions