document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205644>Question 1205644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the function f has a domain of {x ∈ R | x ≥  -  14} and that the function g has a domain of {x ∈ R | x ≤  -  11}. What is the minimum value in the domain of the function (g + f)(x)? Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842578 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3820)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "This is what the number line diagram looks like for each domain.<BR>\n" );
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document.write( "As the diagram above shows, the two regions overlap for the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14+%3C=+x+%3C=+-11 ALIGN=MIDDLE  ALT=\"-14+%3C=+x+%3C=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x is some real number between -14 and -11 including both endpoints.\r<BR>\n" );
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document.write( "Therefore the domain of (g+f)(x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14+%3C=+x+%3C=+-11 ALIGN=MIDDLE  ALT=\"-14+%3C=+x+%3C=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > which shows that x = -14 is the smallest input allowed for function (g+f)(x).\r<BR>\n" );
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document.write( "Answer: -14<BR>\n" );
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