document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73245>Question 73245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the domain of f(x)=7+ sqrt 3x+21 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52471 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I believe your problem is to find the domain of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=7%2B+sqrt%283x%2B21%29 ALIGN=MIDDLE  ALT=\"f%28x%29=7%2B+sqrt%283x%2B21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The only thing we have to be concerned about in this equation is the quantity inside the <BR>\n" );
document.write( "radical sign.<BR>\n" );
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document.write( "In the real world that quantity cannot be negative because you can't take the square root<BR>\n" );
document.write( "of a negative number.  The quantity can be zero or positive only.<BR>\n" );
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document.write( "Therefore we can set up this equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+21+=+0 ALIGN=MIDDLE  ALT=\"3x+%2B+21+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and we can solve this equation by first subtracting 21 from both sides of the equation to<BR>\n" );
document.write( "eliminate the +21 on the left side.  After this subtraction the equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+-21 ALIGN=MIDDLE  ALT=\"3x+=+-21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, to solve for x, just divide both sides by 3 and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-21%2F3+=+-7 ALIGN=MIDDLE  ALT=\"x+=+-21%2F3+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So x = -7 is a critical point.  What happens if we let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-8 ALIGN=MIDDLE  ALT=\"x+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >?  The term inside the radical<BR>\n" );
document.write( "becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24+%2B+21+=+-3 ALIGN=MIDDLE  ALT=\"-24+%2B+21+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Not good because it's negative.  But what happens if we let<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-6 ALIGN=MIDDLE  ALT=\"x+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >?  The term inside the radical becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18%2B21+=+3 ALIGN=MIDDLE  ALT=\"-18%2B21+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. That's OK!<BR>\n" );
document.write( ". <BR>\n" );
document.write( "From this exercise we can gather that x must be at least -7, but it can be a more positive<BR>\n" );
document.write( "value than that.  We can write this inequality as:<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;\" ><BR>\n" );
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document.write( "and we can say that the domain of x is all real values from and including -7 outward to <BR>\n" );
document.write( "positive infinity.<BR>\n" );
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document.write( "Hope this gives you a feel for how domain problems such as these can be done.  Start by<BR>\n" );
document.write( "looking for something that is not mathematically allowed such as square roots of negative<BR>\n" );
document.write( "numbers, divisions by zero, or something similar. The find a way to avoid that situation<BR>\n" );
document.write( "by defining limits on x.<BR>\n" );
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