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<p style="line-height: 150%" align="center">本节习题</p>
<p style="line-height: 150%"><span>1.下列关系中哪一些能够构成函数?<br>
<span>(a)<img src="image/R1.gif" width="13" height="15">
={<<img src="image/x1.GIF" width="11" height="11">,<img src="image/x2.GIF" width="12" height="11">>|(<img src="image/x1.GIF" width="11" height="11">,<img src="image/x2.GIF" width="12" height="11"><img src="image/shuyu.gif" width="13" height="11">N)<img src="image/hequ.gif" width="9" height="11">(<img src="image/x1.GIF" width="11" height="11">+<img src="image/x2.GIF" width="12" height="11"><10)}<br>
<span>(b)<img src="image/R2.gif" width="14" height="15">={<<img src="image/y1.GIF" width="13" height="11">,<img src="image/y2.GIF" width="14" height="11">>|(<img src="image/y1.GIF" width="13" height="11">,<img src="image/y2.GIF" width="14" height="11"><img src="image/shuyu.gif" width="13" height="11">R)<img src="image/hequ.gif" width="9" height="11">(<img src="image/y2.GIF" width="14" height="11">=<img src="IMAGE/y1de2.gif">)}<br>
<span>(c)<img src="image/R3.gif" width="14" height="15">={<<img src="image/y1.GIF" width="13" height="11">,<img src="image/y2.GIF" width="14" height="11">>|(<img src="image/y1.GIF" width="13" height="11">,<img src="image/y2.GIF" width="14" height="11"><img src="image/shuyu.gif" width="13" height="11">R)<img src="image/hequ.gif" width="9" height="11">(<img src="IMAGE/y2de2.gif">=<img src="IMAGE/y1de2.gif">)} </p>
<p style="line-height: 150%"><span>2.设 I 是整数集合， <img src="IMAGE/I+.gif">
是正整数集合，并且把函数 f:I<img src="image/yunhan.gif" width="15" height="9"><img src="IMAGE/I+.gif">
定义成 f(i)=|2i|+1。试求出函数 f 的值域。 </p>
<p style="line-height: 150%"><span>3.设 E 是全集，ρ(E) 是 E 的幂集。显然，ρ(E)<img src="image/cheng.GIF" width="13" height="14">ρ(E)
是由 E 的子集所构成的所有序偶的集合。再设<span><img src="IMAGE/S1.gif"> <img src="image/shuyu.gif" width="13" height="11">ρ(E)、<span><img src="IMAGE/S2.gif"> <img src="image/shuyu.gif" width="13" height="11">ρ(E)。试把
f：ρ(E)<img src="image/cheng.GIF" width="13" height="14">ρ(E)<img src="image/yunhan.gif" width="15" height="9">ρ(E)
定义成 f(<span><img src="IMAGE/S1.gif"> ,<span><img src="IMAGE/S2.gif"> )
=<span><img src="IMAGE/S1.gif"> <img src="image/jiao.gif" width="14" height="15"><span><img src="IMAGE/S2.gif"> 。试证明函数
f 的陪域与值域相等。 </p>
<p style="line-height: 150%"><span>4.设 R 是实数集合，并且对于 x<img src="image/shuyu.gif" width="13" height="11">R
有函数 f(x)=x+3，g(x)=2x+1 和 h(x)=x/2。试求出合成函数 g<img src="image/juhao.GIF" width="8" height="13">f、f<img src="image/juhao.GIF" width="8" height="13">g、f<img src="image/juhao.GIF" width="8" height="13">f、g<img src="image/juhao.GIF" width="8" height="13">g、f<img src="image/juhao.GIF" width="8" height="13">h、h<img src="image/juhao.GIF" width="8" height="13">g、h<img src="image/juhao.GIF" width="8" height="13">f和f<img src="image/juhao.GIF" width="8" height="13">h<img src="image/juhao.GIF" width="8" height="13">g
. </p>
<p style="line-height: 150%"><span>5.设集合 X={0,1,2} 试求出 <img src="IMAGE/XdeX.gif" width="28" height="20">
中如下的所有函数 f：X<img src="image/yunhan.gif" width="15" height="9">X
：(a) <img src="IMAGE/f(x)de2.gif" width="44" height="24">=f(x)；(b)<img src="IMAGE/f(x)de2.gif" width="44" height="24">=x； </p>
<p style="line-height: 150%"><span>(c)<img src="IMAGE/f3(x).gif" width="46" height="32">=x。
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