document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57656>Question 57656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the following functions are inverse.\r<BR>\n" );
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document.write( "f(x) = (8x+9)/8\r<BR>\n" );
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document.write( "g(x) = (10x-7)/8\r<BR>\n" );
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document.write( "I am unable to solve.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #39380 by </B><A HREF=/tutors/aboutme.mpl?userid=hayek><B>hayek(51)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=hayek><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=39380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For g(x) to be an inverse of f(x), the following should be true:<BR>\n" );
document.write( "g(f(x))=x.\r<BR>\n" );
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document.write( "g(f(x)) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%28%288x%2B9%29%2F8%29-7%29%2F8 ALIGN=MIDDLE  ALT=\"%2810%28%288x%2B9%29%2F8%29-7%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2810%2F8%29%28x%2B9%2F8%29-7%2F8 ALIGN=MIDDLE  ALT=\"+%2810%2F8%29%28x%2B9%2F8%29-7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2F8%29x%2B%2890%2F64%29-%287%2F8%29 ALIGN=MIDDLE  ALT=\"%2810%2F8%29x%2B%2890%2F64%29-%287%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This simplifies to a linear equation in x <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.25x%2B.53125 ALIGN=MIDDLE  ALT=\"1.25x%2B.53125\"   DISABLED_style= \"max-width:90%; height:auto;\" > and not simply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so g(x) is not an inverse of f(x).\r<BR>\n" );
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document.write( "Another way to check is graphically.  For g(x) to be an inverse, it should be symmetrical around y=x compared to f(x).  As shown in this chart (where y=x is the blue line), g(x) is not symmetrical around around y=x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-2%2C20%2C-2%2C20%2C%288x%2B9%29%2F8%2C%2810x-7%29%2F8%2C+x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-2%2C20%2C-2%2C20%2C%288x%2B9%29%2F8%2C%2810x-7%29%2F8%2C+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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