Question

The domain of the function $f\left(x\right)={\log }_{10}(\sqrt{x-1}+\sqrt{x-2}+\sqrt{4-x})$ is

• A. $[1,4]$
• B. $[0,4]$
• C. $\left[2.4\right]$
• D. $Noneofthese$

Answer 1

The correct option is C $\left[2.4\right]$

$\begin{array}{c}f\left(x\right)={\log }_{10}\left(\sqrt{x-1}\right)+\sqrt{x-2}+\sqrt{4-x}\\ \Rightarrow \begin{array}{c}10>0\\ 10\ne 1\end{array}\left[{\log }_a^{x}a\ne 1,a>0,x>0\right]\\ \Rightarrow \sqrt{x-1}>0,x>1\\ \Rightarrow \sqrt{x-2}>0,x>2\\ \Rightarrow \sqrt{4-x}>0,4-x>0,x<4\\ domainis\left(2,4\right)Ans.\end{array}$