Q. 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]
Explanation
(a)
For $f(x)$ to be defined
$\ \ \ \ \ \ \ \ \ \ \ \frac{5x - x^{2}}{4} \geq 1 \Rightarrow x^{2} - 5x + 4 \leq 0$
$\Rightarrow (x - 4)(x - 1) \leq 0\ \therefore x \in \lbrack 1,\ 4\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.