Question

The domain of the function $f\left(x\right)=\left[lo{g}_{10}\right(\frac{5x-x^2}{4}){]}^{1/2}$ is

• A. $-\infty <x<\infty$
• B. $1\le x\le 4$
• C. $4\le x\le 16$
• D. $-1\le x\le 1$

Answer 1

The correct option is B $1\le x\le 4$

$lo{g}_{10}\frac{5x-x^2}{4}>0$

$\frac{5x-x^2}{4}\ge 1$

$5x-x^2\ge 4$

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

$(x-4)(x-1)\le 0$

$x$ belongs to $[1,4]$

So the domain is $1\le x\le 4$