Question

The domain of the function $f\left(x\right)=exp\left(\sqrt{5x-3-2x^2}\right)$ is

• A. $[3/2,\infty )$
• B. $[1,3/2]$
• C. $(-\infty ,1]$
• D. $(1,3/2)$

Answer 1

Answer: (B)

We have, $f(x)=$ exp $\left(\sqrt{5x-3-2x^2}\right)$
i.e., $f\left(x\right)=e^{\sqrt{5x-3-2x^2}}$
For Domain of $f\left(x\right),\sqrt{5x-3-2x^2}$ should be +ve.
i.e., $\sqrt{5x-3-2x^2}\ge 0$ (By taking -ve sign common)
$\Rightarrow 2x\left(x-1\right)-3\left(x-1\right)\le 0$
$\Rightarrow \left(2x-3\right)\left(x-1\right)\le 0$
$\Rightarrow 2x-3\le 0$ or $x-1\ge 0$
$\Rightarrow x\le \frac{3}{2}$ or $x\ge 1$
$\therefore 1\le x\le \frac{3}{2}$ i.e., $x\in \left[1,\frac{3}{2}\right]$
Hence, domain of the given function is $[1,\frac{3}{2}].$