document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106122>Question 1106122</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "find the inverse function for the following\r<BR>\n" );
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document.write( "f(x) = x^2+2x where x is greater than or equal to 0\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721063 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=721063\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> looking for g(x) such that  g(f(x)) = x   (i.e. if g(x) is the inverse function of f(x) then when it is applied to f(x) it should give us back x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+x%5E2+%2B+2x+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+x%5E2+%2B+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+%2B+1+=+x%5E2+%2B+2x+%2B+1+ ALIGN=MIDDLE  ALT=\"+f%28x%29+%2B+1+=+x%5E2+%2B+2x+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28f%28x%29+%2B+1%29+=+x%2B1+ ALIGN=MIDDLE  ALT=\"+sqrt%28f%28x%29+%2B+1%29+=+x%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28f%28x%29%2B1%29+-+1+=+x+ ALIGN=MIDDLE  ALT=\"+sqrt%28f%28x%29%2B1%29+-+1+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The LHS is the g(x) we were seeking, just replace \"f(x)\" with \"x\", and note that the domain for this x is <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;\" > because  f(x) >= 0 for x>=0:  <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++highlight%28g%28x%29+=+-1+%2B+sqrt%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"++highlight%28g%28x%29+=+-1+%2B+sqrt%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <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;\" >\r<BR>\n" );
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document.write( "—<BR>\n" );
document.write( "Check:  g(f(x)) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1+%2B+sqrt%28%28x%5E2%2B2x%29%2B1%29+=+-1+%2B+%28x%2B1%29+=+x+ ALIGN=MIDDLE  ALT=\"+-1+%2B+sqrt%28%28x%5E2%2B2x%29%2B1%29+=+-1+%2B+%28x%2B1%29+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (ok)<BR>\n" );
document.write( "—\r<BR>\n" );
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document.write( " </SPAN>\n" );
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