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Properties of Inequalities

If x∈[-4,-1],...

Question

If $x \in [- 4, - 1]$ ,
then $\frac{1}{x}$ belongs to

A

[- 4, - 1]

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B

[- 1, - \frac{1}{4}]

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C

(- \infty, - 1) \cup (- \frac{1}{4}, \infty)

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D

(- \infty, - \frac{1}{4})

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Solution

The correct option is B $[- 1, - \frac{1}{4}]$
Here, $x \in [- 4, - 1]$
Since, $(- 4) (- 1) > 0$
So, $\frac{1}{x} \in [- 1, - \frac{1}{4}]$

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