document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098187>Question 1098187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Inverse function of f(x) = (x+3)^2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712593 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=712593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let y = f(x).\r<BR>\n" );
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document.write( "the equation becomes y = (x+3)^2.\r<BR>\n" );
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document.write( "replace y with x and x with y to get x = (y+3)^2\r<BR>\n" );
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document.write( "take the square root of both sides of the equation to get plus or minus sqrt(x) = y + 3\r<BR>\n" );
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document.write( "solve for y to get y = -3 plus or minus sqrt(x).\r<BR>\n" );
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document.write( "if they are inverse equations of each other, then the value of y in the original equation should be equal to the value of x in the inverse equation and the value of x in the original equation should be equal to the value of y in the inverse equation.\r<BR>\n" );
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document.write( "your original equation is y = (x+3)^2.\r<BR>\n" );
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document.write( "when x = 6, y = 9^2 = 81\r<BR>\n" );
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document.write( "when x = -6, y = (-3)^2 = 9\r<BR>\n" );
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document.write( "your coordinate pairs from the original equation are (6,81) and (-6,9)\r<BR>\n" );
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document.write( "your corresponding coordinate pairs in the inverse equations should be (81,6) and (9,-6).\r<BR>\n" );
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document.write( "your first inverse equation is y = -3 + sqrt(x).\r<BR>\n" );
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document.write( "when x = 81, y becomes equal to -3 + sqrt(81) which is equal to -3 + 9 which is equal to 6.\r<BR>\n" );
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document.write( "your coordinate pair is therefore (81,6) which is the inverse coordinate pair of (6,81) from the original equation.\r<BR>\n" );
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document.write( "your second inverse equation is y = -3 - sqrt(x).\r<BR>\n" );
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document.write( "when x = 9, y becomes equal to -3 - sqrt(9) which is equal to -3 - 3 which is equal to -6.\r<BR>\n" );
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document.write( "your coordinate pair is therefore (9,-6) which is the inverse coordinate pair of (-6,9).\r<BR>\n" );
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document.write( "you can see what's going on in the following graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/101901.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the original equation is y = (x+3)^2.\r<BR>\n" );
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document.write( "the inverse equations are y = -3 + sqrt(x) and y = -3 - sqrt(x).\r<BR>\n" );
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document.write( "you can see that the inverse equation of y = -3 + sqrt(x) coresponds to the right side of the original equation of y = (x+3)^2.\r<BR>\n" );
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document.write( "you can also see that the inverse equation of y = -3 - sqrt(x) corresponds to the left side of the original equation of y = (x+3)^2.\r<BR>\n" );
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document.write( "note that the inverse equation of y = (x+3)^2 is actually x = (y+3)^2.\r<BR>\n" );
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document.write( "the rest is just solving for y in that equation.\r<BR>\n" );
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