document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179552>Question 1179552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that if f : A → B is a function from A to B, then f ◦ iA = f and iB ◦ f = f.<BR>\n" );
document.write( "(iA: inverse of A). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809115 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Prove that if f : A → B is a function from A to B, then f ◦ iA = f and iB ◦ f = f.<BR>\n" );
document.write( "(iA: inverse of A).<BR>\n" );
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document.write( "Then &nbsp;(f o iA) &nbsp;is identical map of the image of &nbsp;A &nbsp;(which is part of &nbsp;B) &nbsp;to &nbsp;B.\r<BR>\n" );
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document.write( "It is &nbsp;NOT &nbsp;TRUE &nbsp;that &nbsp;&nbsp;(f o iA) = f, &nbsp;&nbsp;as you write in your post.\r<BR>\n" );
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document.write( "Also, &nbsp;then (iA o f) &nbsp;is identical map of &nbsp;A &nbsp;to &nbsp;A.\r<BR>\n" );
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document.write( "It is &nbsp;NOT &nbsp;TRUE &nbsp;that &nbsp;&nbsp;(iB o f) = f, &nbsp;as you write in your post.\r<BR>\n" );
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document.write( "Also, notice that &nbsp;\" iB \" &nbsp;is not defined in this problem and in this post, &nbsp;at all.  \r<BR>\n" );
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document.write( "\" iB  \" &nbsp;is totally fictitious subject, &nbsp;irrelevant to this problem.\r<BR>\n" );
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document.write( "Where, &nbsp;from which source, &nbsp;did you retrieve these incorrect statements ?\r<BR>\n" );
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document.write( "Do you create / compose / invent them on your own ?\r<BR>\n" );
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document.write( "If you retrieve it from some source, &nbsp;then keep in mind that this source is &nbsp;UNTRUSTED.\r<BR>\n" );
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document.write( "Notice that in this my post, &nbsp;I make not only my work as a tutor.\r<BR>\n" );
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document.write( "I make your part of work, &nbsp;too &nbsp;(also), &nbsp;trying to formulate the problem &nbsp;CORRECTLY.\r<BR>\n" );
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document.write( "And the final note.\r<BR>\n" );
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document.write( "Everything what I wrote above, &nbsp;is written under the assumption that  &nbsp;&nbsp;iA &nbsp;is &nbsp;the inverse of &nbsp;A,  &nbsp;<U>as it is stated in your post</U>.\r<BR>\n" );
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document.write( "I think that it is the key error in your post.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If to assume that &nbsp;iA &nbsp;is &nbsp;IDENTICAL &nbsp;map of &nbsp;A &nbsp;to itself,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and if to assume that &nbsp;iB &nbsp;is &nbsp;IDENTICAL &nbsp;map of &nbsp;B &nbsp;to itself,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;then all statements in your post become &nbsp;a) &nbsp;&nbsp;correct and &nbsp;b) &nbsp;&nbsp;self-evident.\r<BR>\n" );
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