Q. 8 - Precalculus Enhanced with Graphing Utilities

Question

True or False The domain and the range of the reciprocal function are the set of all real numbers. 

Step-by-Step Solution

Answer

The statement 'The domain and the range of the reciprocal function are the set of all real numbers.' is false.

Step 1. Given information

We have been given a statement 'The domain and the range of the reciprocal function are the set of all real numbers. '.

We have to tell whether this statement is true or false.

Step 2. Analyze the graph of the reciprocal function

The graph of the reciprocal function $f\left(x\right)=\frac{1}{x}$ is:

It is clear from the graph that the function has domain and range all real numbers except $0$.

Therefore, the given statement is false.