Question

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

• A. [1,4]
• B. [1,0]
• C. [0,5]
• D. [5,0]

Answer 1

Answer: (A)

$\because f(x)=\sqrt{{\log }_{10}\left(\frac{5x-x^2}{4}\right)}$
$\therefore f(x)$ exists only for
$\Rightarrow$
${\log }_{10}\left(\frac{5x-x^2}{4}\right)\ge 0$
$\frac{5x-x^2}{4}\ge 1$
$\Rightarrow x^2-5x+4\le 0$
$\Rightarrow (x-1)(x-4)\le 0$
$\Rightarrow x\in [1,4]$