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)

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