Question

The domain of $f(x)={\text{Cos}}^{-1}\left(\frac{x-3}{2}\right)-{\log }_{10}(4-x)$ is

• A. $(1,4)$
• B. $[1,4)$
• C. $(1,4]$
• D. $[1,4]$

Answer 1

Answer: (B)

Let $f(x)={\cos }^{-1}\left(\frac{x-3}{2}\right)-{\log }_{10}(4-x)$
For domain of ${\log }_{10}(4-x)$
$\Rightarrow 4-x>0$
$\Rightarrow x<4$
For domain of ${\cos }^{-1}\left(\frac{x-3}{2}\right)$
$\Rightarrow -1\le \frac{x-3}{2}\le 1$
$\Rightarrow 1\le x\le 5$
Now domain of $f(x)$ will be $x\in [1,4)$