Question

If $f\left(x\right)=3-x$, where $-4\le x\le 4$, then the domain of $lo{g}_e\left[f\right(x\left)\right]$ is:

• A. $\left[-4,4\right]$
• B. $(-\infty ,3]$
• C. $\left(-\infty ,3\right)$
• D. $[-4,3)$

Answer 1

The correct option is C

$\left(-\infty ,3\right)$

Explanation for the correct option.

$lo{g}_e\left[f\right(x\left)\right]=lo{g}_e\left(3-x\right)$

This function will exist for

$\begin{array}{rcl}3-x& >& 0\\ \Rightarrow 3& >& x\\ \Rightarrow x& <& 3\end{array}$

So, the domain of $lo{g}_e\left[f\right(x\left)\right]$ is $\left(-\infty ,3\right)$

Hence, option C is correct.