Originally Posted by

**novice** I found the following from a book with no proof:

Let $\displaystyle f:A \rightarrow A$ be defined by the formula $\displaystyle f(x)=x$, then $\displaystyle f$ is called the identity function, denoted by $\displaystyle 1$ or by $\displaystyle 1_A$.

Let $\displaystyle f:A \rightarrow B$ and it has the inverse function $\displaystyle f^{-1}:B\rightarrow A$, then $\displaystyle f \circ f^{-1}=1$

Question: Is it true that $\displaystyle f \circ f^{-1}=1$?

Isn't $\displaystyle f(x) \circ f^{-1}(x)=x$?