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 $\cos ^{-1}\left(\frac{x-3}{2}\right)$
$\Rightarrow -1 \leq \frac{x-3}{2} \leq 1$
$\Rightarrow 1 \leq x \leq 5$
Now domain of $f(x)$ will be $x \in[1,4)$