document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073529>Question 1073529</A>: <I><SPAN STYLE=\"word-break: break-all;\">   Given that g(x)=4/x , x is not equal to 0 and fg(x)=2x+3 find the function f.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688337 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</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=688337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That 2x+3 is the PRODUCT of the functions f and g.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=fg%28x%29=f%28x%29g%28x%29=f%28x%29%2A%284%2Fx%29=2x%2B3 ALIGN=MIDDLE  ALT=\"fg%28x%29=f%28x%29g%28x%29=f%28x%29%2A%284%2Fx%29=2x%2B3\"   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%28x%29%2A%284%2Fx%29=2x%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29%2A%284%2Fx%29=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------solve this for f(x).\r<BR>\n" );
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document.write( "You want really the composition <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=2x%2B3 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "(clearer solution method)\r<BR>\n" );
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document.write( "Given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=4%2Fx ALIGN=MIDDLE  ALT=\"g%28x%29=4%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and the FUNCTION COMPOSITION <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=2x%2B3 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, find the function f(x).\r<BR>\n" );
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document.write( "g(x) is used as input into f(x) and the expression for the composition is shown, 2x+3.<BR>\n" );
document.write( "You are given g(x), so substitute for its expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%2Fx%29=2x%2B3 ALIGN=MIDDLE  ALT=\"f%284%2Fx%29=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The input indicated on the left side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fx ALIGN=MIDDLE  ALT=\"4%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but you want to have an input of x, because you want to find f(x).<BR>\n" );
document.write( "What number, r, can you put into 4/x so that the result becomes x?<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fr=x ALIGN=MIDDLE  ALT=\"4%2Fr=x\"   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=%284%2Fr%29%2Ar=x%2Ar ALIGN=MIDDLE  ALT=\"%284%2Fr%29%2Ar=x%2Ar\"   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=4=r%2Ax ALIGN=MIDDLE  ALT=\"4=r%2Ax\"   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=rx=4 ALIGN=MIDDLE  ALT=\"rx=4\"   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=rx%281%2Fx%29=4%281%2Fx%29 ALIGN=MIDDLE  ALT=\"rx%281%2Fx%29=4%281%2Fx%29\"   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=highlight_green%28r=4%2Fx%29 ALIGN=MIDDLE  ALT=\"highlight_green%28r=4%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you want to replace x in the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%2Fx%29=2x%2B3 ALIGN=MIDDLE  ALT=\"f%284%2Fx%29=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4%2Fx ALIGN=MIDDLE  ALT=\"r=4%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "These must be done to both sides of the function equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%2Fr%29=2r%2B3 ALIGN=MIDDLE  ALT=\"f%284%2Fr%29=2r%2B3\"   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%284%2F%284%2Fx%29%29=2%284%2Fx%29%2B3 ALIGN=MIDDLE  ALT=\"f%284%2F%284%2Fx%29%29=2%284%2Fx%29%2B3\"   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%28%284%2F4%29x%29=8%2Fx%2B3 ALIGN=MIDDLE  ALT=\"f%28%284%2F4%29x%29=8%2Fx%2B3\"   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=highlight%28f%28x%29=8%2Fx%2B3%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=8%2Fx%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "The function f(x) is now found.<BR>\n" );
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