document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=643090>Question 643090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me with this problem? I am given the function f(x)= x^2 + 2x + 6 with a domain where x = all real numbers, and x is &#8804; k. F is a one to one function, and I am to determine the greatest possible value of k. When k has that value, I am then to determine the range of f, and then the inverse function f^-1 and state its domain and range. After that I am to graph f(x) and f^-1(x). I believe I know how to find the value of k; it's just asking for the upper limit of the domain of the function given. I think to determine the range you can complete the square and put the equation into standard parabola form and so determine the vertex from that, using the y point of the vertex and the fact that it is either an up/down parabola (I believe this one is up) to find the range. I'm just having trouble finding the inverse function. When I switch the x's and y's from the original equation and try to solve for y I seem to get stuck. I know how to find the domain and range from there and I am fairly certain I can graph the equation. I just need help finding the inverse function. Please help? :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #404375 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=404375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the graph below shows the original equation and its inverse.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B2x%2B6%2C-1%2Bsqrt%28x-5%29%2C-1-sqrt%28x-5%29%2Cx%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the inverse equation is found as follows:<BR>\n" );
document.write( "start with:<BR>\n" );
document.write( "y = x^2 + 2x + 6<BR>\n" );
document.write( "subtract 6 from both sides of the equation to get:<BR>\n" );
document.write( "x^2 + 2x = y - 6<BR>\n" );
document.write( "complete the squares on the left side of the equation to get:<BR>\n" );
document.write( "(x+1)^2 = y - 6 + 1 which becomes:<BR>\n" );
document.write( "(x+1)^2 = y - 5<BR>\n" );
document.write( "take the square root of both sides of the equation to get:<BR>\n" );
document.write( "x+1 = +/- sqrt(y-5)<BR>\n" );
document.write( "+/- means plus or minus<BR>\n" );
document.write( "subtract 1 from both sides of the equation to get:<BR>\n" );
document.write( "x = -1 +/- sqrt(y-5)<BR>\n" );
document.write( "replace x with y and y with x to get:<BR>\n" );
document.write( "y = -1 +/- sqrt(x-5)<BR>\n" );
document.write( "that's your inverse equation as seen on the graph.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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