The range of the function $$y=1x2+2$$

We know that $$x2$$≥$$0$$∀x∈R⇒ $$x2+2$$≥$$2$$,∀x∈R or $$2$$≤$$x2+2$$ $$0$$⇒ $$0$$<$$1x2+2$$≤$$12$$

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The range of the function
$y = \frac{1}{x^{2} + 2}$

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0,12

0,∞

0,12

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detailed solution

Correct option is C

We know that x2≥0∀x∈R⇒ x2+2≥2,∀x∈R or 2≤x2+2<∞⇒ 12≥1x2+2>0⇒ 0<1x2+2≤12

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The range of the function y=1x2+2

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The range of the function
$y = \frac{1}{x^{2} + 2}$