Question

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

• A. $[1,-\frac{3}{2}]$
• B. $[\frac{3}{2},\infty ]$
• C. $[-\infty ,1]$
• D. $[1,\frac{3}{2}]$

Answer 1

The correct option is D

$[1,\frac{3}{2}]$

The polynomial under the square root must be non-negative
$5x-3-2x^2\ge 0$

$2x^2-5x+3\le 0$

$(x-1)(x-\frac{3}{2})\le 0$

So, domain of th function: $[1,\frac{3}{2}]$