The correct option is D [ 12,12] (x/1+x^2) =(1/(1/x)+x) if x gt; #10;0, (1/x)+x ≥ 2 if x lt;0, then (1/x)+x≤ 2 ( 1/2) #10;≤ ...

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Solving Inequalities

Find Range of...

Question

Find Range of $\frac{x}{1 + x^{2}}$

[0, 1]

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[\frac{- 1}{2}, 1]

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[0, 2)

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[\frac{- 1}{2}, \frac{1}{2}]

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Solution

The correct option is D $[\frac{- 1}{2}, \frac{1}{2}]$
$(\frac{x}{1 + x^{2}}) = (\frac{1}{(\frac{1}{x}) + x}) i f x > 0, (\frac{1}{x}) + x \geq 2 i f x < 0, t h e n (\frac{1}{x}) + x \leq - 2 (\frac{- 1}{2}) \leq (\frac{1}{(\frac{1}{x}) + x}) \leq (\frac{1}{2}) H e n c e r a n g e [- 1 / 2, 1 / 2]$

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