Example

What is the domain of the function $\displaystyle F(x) = \frac{x}{(x-7)(5x+3)}$?

Solution

This function $F$ is defined for all real numbers except for those that cause division by zero. We call these the restricted values, and they must be excluded from the domain

The denominator is zero when $x-7=0$ or when $5x+3=0$. The restricted values are $x=7$ and $x=-3/5$.

The domain of $F$ is the set of all real numbers except $x=7$ and $x=-3/5$. That is,