A polynomial function $f (x) = 32 - 2 x^{2}$ is non-negative, then what is the domain of the function ?

(- 4, 4)

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[- 4, 4]

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(- \infty, - 4] \cup [4, \infty)

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(- \infty, 4]

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Solution

The correct option is B $[- 4, 4]$
Given: $f (x) \geq 0$
$\Rightarrow 32 - 2 x^{2} \geq 0 \Rightarrow x^{2} - 16 \leq 0 \Rightarrow (x + 4) (x - 4) \leq 0$

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

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