document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=921397>Question 921397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there, I've been trying and trying this problem with no luck.  Could you help me out with this, please?\r<BR>\n" );
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document.write( "Given the function y=(x-11)^2, where x is less than or equal to 11, find the inverse and its domain. \r<BR>\n" );
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document.write( "I keep getting y=plus or minus sqrt(x)-1 which is incorrect. <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 #558955 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=558955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The domain of the original function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=11 ALIGN=MIDDLE  ALT=\"x%3C=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is given to you and this restriction is made to force f(x) to be one-to-one.\r<BR>\n" );
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document.write( "The range of the original function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=0 ALIGN=MIDDLE  ALT=\"y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is found either through the graph or by knowing that (x-11)^2 is either 0 or positive. You can't square a number and get something negative.\r<BR>\n" );
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document.write( "When you solve for the inverse, you swap x and y and solve for y. Doing that also swaps the domain and range. Why? Because the domain is simply the set of allowed x values (inputs) and the range is the set of possible y values (outputs).\r<BR>\n" );
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document.write( "Again, the domain and range swap. This is important.\r<BR>\n" );
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document.write( "So the inverse will have the domain of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+0 ALIGN=MIDDLE  ALT=\"x+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the range of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+11 ALIGN=MIDDLE  ALT=\"y+%3C=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The range for the inverse is what is important here. \r<BR>\n" );
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document.write( "When you swap x and y, then solve for y, you should get this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%22%22%2B-sqrt%28x%29%2B11 ALIGN=MIDDLE  ALT=\"y+=+%22%22%2B-sqrt%28x%29%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But keep in mind that the range of the inverse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+11 ALIGN=MIDDLE  ALT=\"y+%3C=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means negative y values such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2 ALIGN=MIDDLE  ALT=\"y+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > are possible in the range of the inverse.\r<BR>\n" );
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document.write( "This is only possible if you pick the negative square root. You cannot generate negative y values with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28x%29%2B11 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28x%29%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It's impossible. The two pieces are always positive.\r<BR>\n" );
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document.write( "So the inverse is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x) = -\sqrt{x} + 11\">\r<BR>\n" );
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document.write( "You can rewrite that as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f^{-1}(x) = 11-\sqrt{x}\">\r<BR>\n" );
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document.write( "Let me know if that helps or not. Thanks.\r<BR>\n" );
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document.write( "If you need more help, feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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