document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040341>Question 1040341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can I please have your assistance? Consider f(x) = 2x + 3. Find the inverse of this function. Verbally, compare what f does to x  (\"multiply by 2, then add 3\") to what f -1 does to x.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655153 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=655153\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's the basic outline to finding the inverse.\r<BR>\n" );
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document.write( "Step 1) Replace f(x) with y\r<BR>\n" );
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document.write( "Step 2) Swap x and y\r<BR>\n" );
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document.write( "Step 3) Solve for y\r<BR>\n" );
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document.write( "Let's follow this outline to find the inverse.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2x%2B3 ALIGN=MIDDLE  ALT=\"f%28x%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=y+=+2x%2B3 ALIGN=MIDDLE  ALT=\"y+=+2x%2B3\"   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+=+2y%2B3 ALIGN=MIDDLE  ALT=\"x+=+2y%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Swap x and y. Now we isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3+=+2y%2B3-3 ALIGN=MIDDLE  ALT=\"x-3+=+2y%2B3-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3+=+2y ALIGN=MIDDLE  ALT=\"x-3+=+2y\"   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=2y+=+x-3 ALIGN=MIDDLE  ALT=\"2y+=+x-3\"   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=%282y%29%2F2+=+%28x-3%29%2F2 ALIGN=MIDDLE  ALT=\"%282y%29%2F2+=+%28x-3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x-3%29%2F2 ALIGN=MIDDLE  ALT=\"y+=+%28x-3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So if the original function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2x%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the inverse is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x) = \frac{x-3}{2}\">\r<BR>\n" );
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document.write( "Side note: the notation <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)\"> means \"inverse of f(x)\"\r<BR>\n" );
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document.write( "Now let's compare the verbal descriptions\r<BR>\n" );
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document.write( "Original function f(x): multiply the number (x) by 2, then add 3\r<BR>\n" );
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document.write( "Inverse function <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x)\">: subtract 3 from the number (x), then divide by 2\r<BR>\n" );
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document.write( "Essentially whatever you applied to the original function, you follow in reverse undoing the order and applying the opposite operation (eg: the opposite of addition is subtraction). So if you added 3 to the unknown number, then you undo that by subtracting 3 from the number when it comes to the inverse. In a sense, \"inverse\" means \"opposite\".  </SPAN>\n" );
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