Q 39. - Precalculus Enhanced with Graphing Utilities

Question

Find the domain of the function.

$F\left(x\right)={\log }_2\left(x^2\right)$

Step-by-Step Solution

Answer

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

Step 1. Given information

A logarithmic function is given as $F\left(x\right)={\log }_2\left(x^2\right)$.

Step 2. Formula Used

The domain of the logarithmic function $f\left(x\right)={\log }_a\left(x\right)$ is determined by $x>0$. 

Step 3. Finding The Domain

The function is $F\left(x\right)={\log }_2\left(x^2\right)$

Now, for the domain,

$x^2>0$

For all real $x$, the expression $x^2$ is positive.

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

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