document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=832815>Question 832815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "I am having trouble with this question.\r<BR>\n" );
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document.write( "Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. <BR>\n" );
document.write( "f(x)=3x-7<BR>\n" );
document.write( "g(x)=x+3/7\r<BR>\n" );
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document.write( "I am absolutely lost on how to solve this question. Detailed explanation would be deeply appreciated. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #502195 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=502195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Not sure how you mean your g(x).  As written you have x+3/7, as rendered, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2F7 ALIGN=MIDDLE  ALT=\"x%2B3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3%28g%28x%29%29%2B7=3%28x%2B3%2F7%29-7 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3%28g%28x%29%29%2B7=3%28x%2B3%2F7%29-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B9%2F7-7 ALIGN=MIDDLE  ALT=\"3x%2B9%2F7-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2A7%29%2F7%2B9%2F7-7%2A7 ALIGN=MIDDLE  ALT=\"%283x%2A7%29%2F7%2B9%2F7-7%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2821x%2B9-7%29%2F7 ALIGN=MIDDLE  ALT=\"%2821x%2B9-7%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2821x%2B2%29%2F7 ALIGN=MIDDLE  ALT=\"%2821x%2B2%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Will that composition give x as the result?<BR>\n" );
document.write( "NO.\r<BR>\n" );
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document.write( "You likely misunderstood what you read of g(x).<BR>\n" );
document.write( "This definition is different:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x%2B3%29%2F7 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x%2B3%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Is this what you are really given?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3%28%28x%2B3%29%2F7%29-7 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3%28%28x%2B3%29%2F7%29-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B3%29%2F7-7%2A7%2F7 ALIGN=MIDDLE  ALT=\"3%28x%2B3%29%2F7-7%2A7%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B9%29%2F7-49%2F7 ALIGN=MIDDLE  ALT=\"%283x%2B9%29%2F7-49%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B9-49%29%2F7 ALIGN=MIDDLE  ALT=\"%283x%2B9-49%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-40%29%2F7 ALIGN=MIDDLE  ALT=\"%283x-40%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Neither is this one x.<BR>\n" );
document.write( "NOT the inverse of f(x).\r<BR>\n" );
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document.write( "The basic idea is if f(g(x))=x and g(f(x))=x, then f and g are inverses.\r<BR>\n" );
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document.write( "If you WANT to know the inverse of f(x), then try:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=highlight_green%28x=3%28g%28x%29%29-7%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=highlight_green%28x=3%28g%28x%29%29-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve this for g(x).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B7=3%2Ag%28x%29%29 ALIGN=MIDDLE  ALT=\"x%2B7=3%2Ag%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%2F3=%281%2F3%29%283%29g%28x%29 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%2F3=%281%2F3%29%283%29g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%2F3=g%28x%29 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%2F3=g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----------This is likely to be the inverse of f(x). </SPAN>\n" );
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