document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=899350>Question 899350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain of the function. State the domain in interval notation for<BR>\n" );
document.write( "f(x)=square root of 3x^2-x-2<BR>\n" );
document.write( "I know you have to look for restrictions but I'm not sure what to do with this type of problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #545305 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=545305\">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=f%28x%29=sqrt%283x%5E2-x-2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=sqrt%283x%5E2-x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The restriction starts with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-x-2%3E=0 ALIGN=MIDDLE  ALT=\"3x%5E2-x-2%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "which leads to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29%28x-1%29%3E=0 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%28x-1%29%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "whose critical points are at -2/3 and 1.\r<BR>\n" );
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document.write( "You can test the signs around the critical values for x and find that the acceptable values for x are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-2%2F3 ALIGN=MIDDLE  ALT=\"x%3C=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%3C=x ALIGN=MIDDLE  ALT=\"1%3C=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  No values of x between the critical points are acceptable in the function because they force square root of a negative number  (which makes for complex solutions containing imaginary numbers). </SPAN>\n" );
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