document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=323243>Question 323243</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have 20 algebra problems, some of which are to \"simplify,\" \"solve,\" and to \"evaluate.\" What I need is a way to double check my work. Here are a couple of examples; find inverse funtion of (x),  f(x)=4x-8, my answer is f, raised to the negative 1 power(x)= x+2\r<BR>\n" );
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document.write( "Another problem is find inverse of, g(x)=7 raised to the \"x\" power, my answer is g raised to the negative 1 power(x)= the 7th root of x.\r<BR>\n" );
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document.write( "Another example is to evaluate; 3 natural log (e cubed) my answer is 9.\r<BR>\n" );
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document.write( "Any feedback would be greatly appreciated. Thank you for your time.\r<BR>\n" );
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document.write( "Margie </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #231370 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=231370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To check if a function is the inverse of another function, we use the property <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(f^{-1}(x))=x\"> and we also use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(f(x))=x\">. We have to check both equations. \r<BR>\n" );
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document.write( "Since we're given that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)=4x-8\"> and you claim that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)=x+2\">, this means that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(f^{-1}(x))=4(x+2)-8=4x+8-8=4x\"> which is NOT equal to 'x'. So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)=x+2\"> is not correct.\r<BR>\n" );
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document.write( "Let's find the inverse of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)=4x-8\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)=4x-8\"> Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x-8 ALIGN=MIDDLE  ALT=\"y=4x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace f(x) with y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4y-8 ALIGN=MIDDLE  ALT=\"x=4y-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Swap x and y. The goal now is to solve for y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B8=4y ALIGN=MIDDLE  ALT=\"x%2B8=4y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 8 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B8%29%2F4=y ALIGN=MIDDLE  ALT=\"%28x%2B8%29%2F4=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 to isolate y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B8%29%2F4 ALIGN=MIDDLE  ALT=\"y=%28x%2B8%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2F4%2B8%2F4 ALIGN=MIDDLE  ALT=\"y=x%2F4%2B8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F4%29x%2B2 ALIGN=MIDDLE  ALT=\"y=%281%2F4%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce and simplify.\r<BR>\n" );
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document.write( "So the inverse function of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)=4x-8\"> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)=\frac{1}{4}x+2\">\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Let's first see if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(f^{-1}(x))=x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)=4x-8\"> ... Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(f^{-1}(x))=4\left(\frac{1}{4}x+2\right)-8\"> ... Plug in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)=\frac{1}{4}x+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(f^{-1}(x))=4\left(\frac{1}{4}x\right)+4\left(2\right)-8\"> ... Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(f^{-1}(x))=\frac{4}{4}x+8-8\"> ... Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(f^{-1}(x))=\frac{4}{4}x\"> ... Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(f^{-1}(x))=x\"> ... Reduce.\r<BR>\n" );
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document.write( "Now let's see if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(f(x))=x\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)=\frac{1}{4}x+2\"> ... Start with the inverse function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(f(x))=\frac{1}{4}(4x-8)+2\"> ... Plug in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)=4x-8\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(f(x))=\frac{1}{4}(4x)+\frac{1}{4}(-8)+2\"> ... Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(f(x))=\frac{4x}{4}+\frac{-8}{4}+2\"> ... Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(f(x))=x-2+2\"> ... Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(f(x))=x\"> ... Combine like terms.\r<BR>\n" );
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document.write( "So we've shown that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(f^{-1}(x))=x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(f(x))=x\">\r<BR>\n" );
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document.write( "So this verifies that the inverse function of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)=4x-8\"> is indeed <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)=\frac{1}{4}x+2\"> </SPAN>\n" );
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