Q 47. - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of the function :  $f\left(x\right)=\sqrt{\ln \left(x\right)}$

Step-by-Step Solution

Answer

The domain of the given function is :  $[1,\infty )$

Step 1. Given information

Given expression is $f\left(x\right)=\sqrt{\ln \left(x\right)}$

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

Step 2. Find domain

The logarithm of zero and a negative number is invalid, therefore the 

The domain of the given function is : $[1,\infty )$

Step 3. Check

$\ln \left(0\right)$ is undefined and the logarithm of a negative number is undefined.

Hence, the domain of the function is $\{x\in R : x\ge 1\}$