Question

The domain of the function, $y=f\left(x\right)=\sqrt{{\log }_{10}\left(\frac{5x-x^2}{4}\right)}$ is

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

Answer 1

The correct option is A $[1,4]$

Given,

$y=f\left(x\right)=\sqrt{{\log }_{10}\left(\frac{5x-x^2}{4}\right)}$

For given function to be defined,
${\log }_{10}\left(\frac{5x-x^2}{4}\right)\ge 0\Rightarrow \left(\frac{5x-x^2}{4}\right)\ge {10}^0=1$

$\Rightarrow 5x-x^2\ge 4\Rightarrow x^2-5x+4\le 0$

$\Rightarrow (x-1)(x-4)\le 0\Rightarrow x\in [1,4]$