Question

Find the domain of $f(x)=\sqrt (x2+4x−2x2−3)$f(x)=x2+4x−2x2−3

• A. $[3,5]$
• B. $[-3,-1]$
• C. $[-1,0]$
• D. $[1,3]$

Answer 1

The correct option is D $[1,3]$

For given function to be defined,
$x^2+4x\ge 2x^2+3\Rightarrow x^2-4x+3\le 0$
$\Rightarrow (x-3)(x-1)\le 0\Rightarrow x\in [1,3]$