M7MBA wrote: ↑

Sun Jun 21, 2020 2:11 pm

If \(-1 < x < 0,\) which of the following is correct?

A. \(x^{−3} < x^{−2} < x^{−1}\)

B. \(x^{−1} < x^{−2} < x^{−3}\)

C. \(x^{−1} < x^{−3} < x^{−2}\)

D. \(x^{−2} < x^{−3} < x^{−1}\)

E. \(x^{−3} < x^{−1} < x^{−2}\)

[spoiler]OA=E[/spoiler]

Source: Magoosh

Let's assume a suitable value within the range of \(-1 < x < 0\). Say \(x=-1/3\)

So, we have

\(x^{−1}= {(-1/3)}^{(-1)} = -3\);
\(x^{−2}= {(-1/3)}^{(-2)} = 9\);
\(x^{−3}= {(-1/3)}^{(-3)} = -27\)

We see that\(x^{−3} < x^{−1} < x^{−2}\), i.e. option E.

Correct answer: E

Hope this helps!

-Jay
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