Question

If the polynomial function $f\left(x\right)=32-2x^2$ is non-negative, then $x\in$

• A. $(-\infty ,-4]\cup [4,\infty )$
• B. $(-4,4)$
• C. $[-4,4]$
• D. $(-\infty ,4]$

Answer 1

The correct option is C $[-4,4]$

Given, $f\left(x\right)\ge 0$
$\Rightarrow 32-2x^2\ge 0\Rightarrow x^2-16\le 0\Rightarrow (x+4)(x-4)\le 0$


By wavy-curve method,
$x\in [-4,4]$