document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102559>Question 102559</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain of f(x)= 7+ the square root of 3x+21, and express it using interval notation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74575 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=74575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7%2Bsqrt%283x%2B21%29 ALIGN=MIDDLE  ALT=\"y=7%2Bsqrt%283x%2B21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "Remember you cannot take the square root of a negative value. So that means the argument <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B21 ALIGN=MIDDLE  ALT=\"3x%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be greater than or equal to zero (i.e. the argument <font size=4><b>must</b></font> be positive)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B21%3E=0 ALIGN=MIDDLE  ALT=\"3x%2B21%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the inner expression greater than or equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%3E=0-21 ALIGN=MIDDLE  ALT=\"3x%3E=0-21\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 21 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%3E=-21 ALIGN=MIDDLE  ALT=\"3x%3E=-21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=%28-21%29%2F%283%29 ALIGN=MIDDLE  ALT=\"x%3E=%28-21%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3 to isolate x \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=-7 ALIGN=MIDDLE  ALT=\"x%3E=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So that means x must be greater than or equal to -7\r<BR>\n" );
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document.write( "So here is the domain in interval notation: [-7,<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \infty\">)\r<BR>\n" );
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document.write( "Notice if we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7%2Bsqrt%283x%2B21%29 ALIGN=MIDDLE  ALT=\"y=7%2Bsqrt%283x%2B21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-2%2C+18%2C+7%2Bsqrt%283x%2B21%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-2%2C+18%2C+7%2Bsqrt%283x%2B21%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > notice how the graph never crosses the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this graphically verifies our answer.\r<BR>\n" );
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document.write( "and we can see that x must be greater than or equal to -7 in order to lie on the graph<BR>\n" );
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