document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285588>Question 285588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What's the domain of f+g when f(x)=2x-5 and g(x)= square root x+6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207016 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=207016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (f+g)(x) = f(x) + g(x)\r<BR>\n" );
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document.write( "f(x) = 2x-5<BR>\n" );
document.write( "g(x) = sqrt(x+6)\r<BR>\n" );
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document.write( "(f+g)(x) = (2x-5) + sqrt(x+6)\r<BR>\n" );
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document.write( "The only restriction on the domain of this function is the square root of (x+2^ can't be negative.\r<BR>\n" );
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document.write( "to find out when sqrt(x+6) goes negative, use the equation:\r<BR>\n" );
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document.write( "(x+6) < 0\r<BR>\n" );
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document.write( "Subtract x from this equation to get x < -6\r<BR>\n" );
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document.write( "When x < -6, the square root of (x+6) goes negative and the domain goes invalid.\r<BR>\n" );
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document.write( "The domain of (f+g)(x) is therefore all values of x >= -6\r<BR>\n" );
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document.write( "Note that this i also the domain of g(x).\r<BR>\n" );
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document.write( "The domain of f(x) is all real value of x.\r<BR>\n" );
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document.write( "(f+g)(x) adds f(x) plus g(x) together so the domain becomes the more restrictive of the two which is the domain of g(x).\r<BR>\n" );
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document.write( "A graph of the equation (f+g)(x) = (2x-5) + sqrt(x+6) is shown below:\r<BR>\n" );
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document.write( "You can see that the graph stops at x = -6 and doesn't go any further.\r<BR>\n" );
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document.write( "That's because the value of y when x < -6 is not a real number and is therefore undefined.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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