<p>Each of the following inequalities is true for some values of x EXCEPT</p>
<p>a) x < x^2 < x^2
b) x < x^3 < x^2
c) x^2 < x^3 < x
d) x^3 < x < x^2
e) x^3 < x^2 < x</p>
<p>Can someone please explain the answer? BTW, what type of question is this because this is the question type I have most trouble with.</p>
<p>Did you copy the question correctly? Otherwise a is wrong because x^2 will never be greater than x^2 for any value.</p>
<p>I’m guessing OP meant a) x<x^2<x^3</p>
<p>Which is possible. My suggestion would be to graph all of them and establish the four relationships, since there are only four, if you don’t see it intuitively.</p>
<p>The only one that is never possible is C.</p>
<p>Whoops, a is x < x^2 < x^3. Graphing seems like too much under time constraint.</p>
<p>Those are really basic functions; but if not by hand, you should have a graphing calculator. Graph all three on top of each other and then establish relationships.</p>
<p>Me being stupid.</p>
<p>^Not when -1<x<0</p>
<p>Answer is C then. My bad.</p>
<p>x^2 < x^3 < x</p>
<p>Reason: If x is positive, x^3 is bigger than x. If x is negative, x^2 is bigger.</p>
<p>@olleger : What about choice E</p>
<p>put a positive number less than 1 and e works</p>
<p>OK, thanks for the help!</p>