Question

The domain of the function $f\left(x\right)=exp\left(\sqrt{5x-3-2x^2}\right)$ 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 $[1,\frac{3}{2}]$

R.E.F image

The domain of the function

$f\left(x\right)=exp\left(\sqrt{5x-3-2x^2}\right)$

Exp $\int$n is defined every where

or redouble line

then

for $\sqrt{5x-3-2x^2}$ to be value

$5x-3-2x^2\ge 0$

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

& $x=\frac{-5\pm \sqrt{25-4(-2)(-3)}}{2x(-2)}$

$=\frac{-5\pm \sqrt{25-24}}{-4}=\frac{-5+1}{-4},\frac{-5-1}{-4}$

$=\frac{-4}{-4},\frac{-6}{-4}$

$=1,1.5$

So $5x-3-2x^2\ge 0$

$\Rightarrow (x-1)(x-1.5)\ge 0$

Domain $=(-\infty ,1)\cup (3/2,\infty )$

(1) one and $\frac{3}{2}$ and including

in domain