Q 48. - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of the function :  $g\left(x\right)=\frac{1}{\ln \left(x\right)}$

Step-by-Step Solution

Answer

The domain of the given function is : $(0,\infty )-\left\{1\right\}$

Step 1. Given information

Given expression is  $g\left(x\right)=\frac{1}{\ln \left(x\right)}$

Domain : The range of $x$ is known as domain of definition.

Step 2. Find domain

Here, the range of the domain of definition should be $\frac{1}{\ln \left(x\right)}>0$, to achieve the finite values of the functions.

Hence, $\ln \left(x\right)$ may have all real value except $0$.

Therefore, the domain of the given function is :  $(0,\infty )-\left\{1\right\}$