Chapter 11.7, Problem 9P

Find the domain for x in the equation $xy=1$.

To determine

To find : the domain for $x$

Answer to Problem 9P

The domain for $x$ is $x\in \left(-\infty ,0\right)\cup \left(0,\infty \right)$

Explanation of Solution

Given information : The equation is $xy=1$

Calculation :

The domain for $x$ in $xy=1$

  $\begin{array}{l}xy=1\\ y=\frac{1}{x}\end{array}$

The denominator cannot be zero

Thus, $z\ne 0$

The domain will contain all values of $x$ except zero

  $\therefore x\in \left(-\infty ,0\right)\cup \left(0,\infty \right)$