document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145524>Question 145524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am working with Inverse functions and need help find (f(g))(x) and (g(f))(x) given f(x)=log(2)x g(x)=2 to x power<BR>\n" );
document.write( "sorry if that is written confusing.. on paper the 2 after log is lowered  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106173 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=106173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's evaluate f(g(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=log%282%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=log%282%2C%28x%29%29\"   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=log%282%2C%282%5Ex%29%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=log%282%2C%282%5Ex%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=2%5Ex ALIGN=MIDDLE  ALT=\"g%28x%29=2%5Ex\"   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=x%2Alog%282%2C%282%29%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=x%2Alog%282%2C%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the right side using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%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=f%28g%28x%29%29=x%2A1 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=x%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the log base 2 of 2 to get 1. Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2C%28x%29%29=1 ALIGN=MIDDLE  ALT=\"log%28x%2C%28x%29%29=1\"   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=x ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "Let's evaluate g(f(x))\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=2%5Ex ALIGN=MIDDLE  ALT=\"g%28x%29=2%5Ex\"   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=2%5E%28log%282%2C%28x%29%29%29 ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=2%5E%28log%282%2C%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=log%282%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=log%282%2C%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=log%282%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"y=log%282%2C%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ey=x ALIGN=MIDDLE  ALT=\"2%5Ey=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > by use of the property <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29=y ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > ====> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Ey=x ALIGN=MIDDLE  ALT=\"b%5Ey=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=g%28f%28x%29%29=2%5Ey ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=2%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%29%29 ALIGN=MIDDLE  ALT=\"log%282%2C%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with \"y\"\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;\" > Now replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ey ALIGN=MIDDLE  ALT=\"2%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" > with \"x\"\r<BR>\n" );
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document.write( "So <b>both</b> f(g(x)) and g(f(x)) equal x. </SPAN>\n" );
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