Chapter 9 - Section 9.2 - Composite and Inverse Functions - Exercise Set - Page 690: 100

False

The statement is false. A one-to-one function is a function that maps no two elements of its domain to a single value in range. Thus, the function $f(x)=5$ maps every element in the domain to $5$. Therefore, $f(x)=5$ is not one-to-one function.