Question

If $f\left(x\right)=\sqrt{2-x}$ and $g\left(x\right)=\sqrt{1-2x},$ then the domain of $log\left(x\right)$ is :

• A. $(-\infty ,1/2]$
• B. $(1/2,\infty ]$
• C. $(-\infty ,3/2]$
• D. None of these

Answer 1

The correct option is A $(-\infty ,1/2]$

$f\left(x\right)=\sqrt{2-x}g\left(x\right)=\sqrt{1-2x}$

Domain of $\mathrm{fog}\left(x\right)$ is equal to the domain of $g\left(x\right)$

$\begin{array}{c}1-2x\ge 0\\ x\le \frac{1}{2}\end{array}$

$x\in (-\infty ,\frac{1}{2}]$