Solution 2.3:10c

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The expression
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The expression <math>1\ge x\ge y^{2}</math> means that we have a region which is defined by the two inequalities <math>1\ge x</math> and <math>x\ge y^{2}</math>. The first inequality gives us the region to the left of the line <math>x=1</math>. If the other inequality had been instead <math>y\ge x^{2}</math>, we would have a region above the parabola <math>y=x^{2}</math>, but in our case ''x'' and ''y'' have reversed roles, so the inequality <math>x\ge y^{2}</math> defines the same type of parabolic region, but with the ''x''- and ''y''-axes having changed place.
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<math>\text{1}\ge x\ge \text{ }y^{\text{2}}</math>
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means that we have a region which is defined by the two inequalities
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<math>\text{1}\ge x\text{ }</math>
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{| align="center"
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and
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|align="center"|[[Image:2_3_10_c1-1.gif|center]]
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<math>x\ge \text{ }y^{\text{2}}</math>. The first inequality gives us the region to the left of the line
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|width="10px"|&nbsp;
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<math>x=\text{1}</math>. If the other inequality had been instead
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|align="center"|[[Image:2_3_10_c1-2.gif|center]]
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<math>y=x^{\text{2}}</math>, we would have a region above the parabola
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<math>y=x^{\text{2}}</math>, but in our case
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|align="center"|<small>The region 1&nbsp;≥&nbsp;''x''</small>
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<math>x</math>
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and
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|align="center"|<small>The region ''x''&nbsp;≥&nbsp;''y''²</small>
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<math>y</math>
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|}
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have reversed roles, so the inequality
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<math>x\ge \text{ }y^{\text{2}}</math>
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defines the same type of parabolic region, but with the
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<math>x</math>
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<math>y</math>
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-axes having changed place.
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[[Image:2_3_10_c1.gif|center]]
 
Together, the inequalities define the region that is bordered on the left by the parabola and on the right by the line.
Together, the inequalities define the region that is bordered on the left by the parabola and on the right by the line.
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[[Image:2_3_10_c2.gif|center]]
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{| align="center"
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|align="center"|[[Image:2_3_10_c2.gif|center]]
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|-
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|align="center"|<small>The region 1&nbsp;≥&nbsp;''x''&nbsp;≥&nbsp;''y''²</small>
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|}

Current revision

The expression \displaystyle 1\ge x\ge y^{2} means that we have a region which is defined by the two inequalities \displaystyle 1\ge x and \displaystyle x\ge y^{2}. The first inequality gives us the region to the left of the line \displaystyle x=1. If the other inequality had been instead \displaystyle y\ge x^{2}, we would have a region above the parabola \displaystyle y=x^{2}, but in our case x and y have reversed roles, so the inequality \displaystyle x\ge y^{2} defines the same type of parabolic region, but with the x- and y-axes having changed place.


 
The region 1 ≥ x The region x ≥ y²


Together, the inequalities define the region that is bordered on the left by the parabola and on the right by the line.


The region 1 ≥ x ≥ y²
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