Chapter 1 - Functions and Their Graphs - Section 1.4 Library of Functions; Piecewise-defined Functions - 1.4 Assess Your Understanding - Page 85: 8

False

The reciprocal function $f(x)=\dfrac{1}{x}$ is not defined for $x=0$. This is because division by zero is not allowed. That is, $f(x)=\dfrac{1}{0}= \ undefined$ Therefore, the domain for the reciprocal function is not the set of all real numbers. Rather, the domain is all real numbers except $x=0$. Thus, the statement is False.