Q. - Precalculus Enhanced with Graphing Utilities

Question

The domain of $\frac{f}{g}$ consists of numbers $x$ for which $g\left(x\right)$ ____ $0$ that are in the domains of both ____ and ____.

Step-by-Step Solution

Answer

The domain of $\frac{f}{g}$ consists of numbers $x$ for which $g\left(x\right)\ne 0$that are in the domains of both $\mathit{f}$ and .

Step 1. Given information

The domain of $\frac{f}{g}$ consists of numbers $x$ for which $g\left(x\right)$ ____ $0$ that are in the domains of both ____ and ____.

Step 2. DEFINITION

The quotient $\frac{f}{g}$ is the function defined by

$\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)} g\left(x\right)\ne 0$

Step 3. The answer is,

The domain of $\frac{f}{g}$ consists of numbers $x$ for which $g\ne 0$ that are in the domains of both $f$ and $g$.