Q 43. - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of the function.

$g\left(x\right)=\ln \left(\frac{1}{x+1}\right)$

Step-by-Step Solution

Answer

The domain of the given function $f\left(x\right)$ is $\left(-1,\infty \right)$

Step 1. Given information

A logarithmic function is given as  $f\left(x\right)=\ln \left(\frac{1}{x+1}\right)$

Step 2. Formula Used

The domain of the logarithmic function $f\left(x\right)=\ln \left(x\right)$ is determined by $x>0$

Step 3. Finding The Domain

The function is $f\left(x\right)=\ln \left(\frac{1}{x+1}\right)$

Now, for the domain,

$\frac{1}{x+1}>0$

On solving

$$\begin{gathered} \frac{x+1}{{\left(x+1\right)}^2}>0 \\ x+1>0 \\ x>-1 \end{gathered}$$

The required domain of $f\left(x\right)$, using

interval notation, is $\left(-1,\infty \right)$.