document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091038>Question 1091038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6.Find the inverse of the following function:f(x)=x^2+4/3.<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 #705477 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=705477\">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( "start with y = x^2 + 4/3.\r<BR>\n" );
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document.write( "replace y with x and x with y to get x = y^2 + 4/3\r<BR>\n" );
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document.write( "subtract 4/3 from both sides of the equation to get x - 4/3 = y^2\r<BR>\n" );
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document.write( "take the square root of both sides of the equation to get y = plus or minus square root of (x - 4/3)\r<BR>\n" );
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document.write( "that should be your answer.\r<BR>\n" );
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document.write( "y = plus or minus sqrt(x - 4/3)\r<BR>\n" );
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document.write( "to show that these are inverse equations, then graph the original equation and graph the two inverse equations and then graph the line y = x and then graph the line y = -x + 5\r<BR>\n" );
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document.write( "if the equations are inverse, then they should be reflections about the line y = x.\r<BR>\n" );
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document.write( "if they are reflections about the line y = x, then their coordinates are interposed.\r<BR>\n" );
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document.write( "(x,y) on one side of the line y = x is the same distance from (y,x) on the other side of the line y = x.\r<BR>\n" );
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document.write( "this can be shown on the graph by using their intersections with the line y = -x + 5, with the 5 being arbitrarily chosen for clarity.\r<BR>\n" );
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document.write( "the graph is shown below:\r<BR>\n" );
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document.write( "you can see that the red line and blue line are reflections about the line y = x and you can see that the red line and the orange line are reflections about the line y = x.\r<BR>\n" );
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document.write( "the red line is y = x^2 + 4/3\r<BR>\n" );
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document.write( "the blue line is y = sqrt(x - 4/3)\r<BR>\n" );
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document.write( "the orange line is y = -sqrt(x - 4/3)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/082101.jpg\" alt = \"$$$\" </>\r<BR>\n" );
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