Q. The domain of the function $f(x) = \exp{(\sqrt{5x - 3 - 2x^{2}})}$ is
A) $\lbrack 3/2,\ \infty)$
B) $\lbrack 1,\ 3/2\rbrack$
C) $( - \infty,\ 1)$
D) (1, 3/2)
Explanation
(b)
Given, $f(x) = e^{\sqrt{5x - 3 - 2x^{2}}}$
For domain of $f(x)$
$\ \ \ \ \ \ \ \ \ \ \ \ 2x^{2} - 5x + 3 \leq 0$
$\Rightarrow \ \ (2x - 3)(x - 1) \leq 0$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1 \leq x \leq \frac{3}{2}$
$\therefore$ Domain of $f(x) = \left\lbrack 1,\ \frac{3}{2} \right\rbrack$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.