document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192113>Question 192113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use composition of functions to show that the functions f(x) = 5x – 2 and g(x) = (x+2)/5 are inverse functions. That is, show that (f of g)(x)=x and show that (g of f)(x) =x \r<BR>\n" );
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document.write( "I am not sure how to approach this assignment!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144175 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=144175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: (f o g)(x) means f(g(x)) and (g o f)(x) means g(f(x))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=5x-2 ALIGN=MIDDLE  ALT=\"f%28x%29=5x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first function\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=5%28%28x%2B2%29%2F5%29-2 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=5%28%28x%2B2%29%2F5%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x%2B2%29%2F5 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x%2B2%29%2F5\"   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=cross%285%29%28%28x%2B2%29%2Fcross%285%29%29-2 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=cross%285%29%28%28x%2B2%29%2Fcross%285%29%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out like terms\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=x%2B2-2 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=x%2B2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\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=x ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x%2B2%29%2F5 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x%2B2%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29=%28%285x-2%29%2B2%29%2F5 ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=%28%285x-2%29%2B2%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=5x-2 ALIGN=MIDDLE  ALT=\"f%28x%29=5x-2\"   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=g%28f%28x%29%29=%285x%29%2F5 ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=%285x%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29=%28cross%285%29x%29%2Fcross%285%29 ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=%28cross%285%29x%29%2Fcross%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29=x ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Since we've shown that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=x ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29=x ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the two functions are inverses of each other.<BR>\n" );
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