First slide

Functions (XII)

Question

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

Easy

A

$[0, \frac{1}{2}]$
B

$(0, \infty)$
C

$(0, \frac{1}{2}]$
D

None of these

Solution

$We know that x^{2} \geq 0 \forall x \in R$
$\begin{array}{l} \Rightarrow x^{2} + 2 \geq 2, \forall x \in R \\ or 2 \leq (x^{2} + 2) < \infty \\ \Rightarrow \frac{1}{2} \geq \frac{1}{x^{2} + 2} > 0 \\ \Rightarrow 0 < \frac{1}{x^{2} + 2} \leq \frac{1}{2} \end{array}$

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