Chapter 6.3, Problem 1AYU

The domain of the function $f(x)\text{=}\frac{x\text{+}\text{1}}{2x\text{+}\text{1}}$ is _____ . (pp.64-66)

To determine

To fill: The domain of the function $f\left(x\right)=\frac{x+1}{2x+1}$ is ___________.

Answer to Problem 1AYU

Solution:

$\left\{x|x\ne -\frac{1}{2}\right\}$

Explanation of Solution

The function $g$ says to divide $x+1$ by $2x+1$. Since division by $0$ is not defined, the denominator $2x+1$ can never be zero, so $x$ can never equal $-\frac{1}{2}$. The domain of the function $f$ is $\left\{x|x\ne -\frac{1}{2}\right\}$.