document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6671>Question 6671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve this function of operations:<BR>\n" );
document.write( "Given:f(x) =  x^2 - 4 (x squared minus 4) and g(x) = radical 2x + 4<BR>\n" );
document.write( "Solve: Domain of f(g(x))\r<BR>\n" );
document.write( "\n" );
document.write( "I understand that I have to plug in g(x) into f(x) but I don't understand the part about the Domain. Please help me. Thanks.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3673 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=3673\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm thinking that you meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%28x%29+=+sqrt%282x+%2B+4%29+ ALIGN=MIDDLE  ALT=\"+g%28x%29+=+sqrt%282x+%2B+4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If you plug that into f(x), you'll get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28g%28x%29%29+=+%28g%28x%29%29%5E2+-+4+=+%28sqrt%282x+%2B+4%29%29%5E2+-+4+=+2x+%2B+4+-+4+=+2x+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28g%28x%29%29+=+2x+ ALIGN=MIDDLE  ALT=\"+f%28g%28x%29%29+=+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- The domain would have to be the set of values that you could plug into f(g(x)) legally. In other words, what values of x can we put into the function so that none of those values will make a denominator zero, or whatever inside the square root \"house\" negative. In this case, you can choose any x value you want, since you can multiply 2 times any number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Say that you meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g%28x%29+=+sqrt%282x%29+%2B+4+ ALIGN=MIDDLE  ALT=\"+g%28x%29+=+sqrt%282x%29+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If you plug that into f(x), you'll get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28g%28x%29%29+=+%28g%28x%29%29%5E2+-+4+=+%28sqrt%282x%29+%2B+4%29%5E2+-+4+ ALIGN=MIDDLE  ALT=\"+f%28g%28x%29%29+=+%28g%28x%29%29%5E2+-+4+=+%28sqrt%282x%29+%2B+4%29%5E2+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28g%28x%29%29+=+%28sqrt%282x%29+%2B+4%29%28sqrt%282x%29+%2B+4%29+-+4+ ALIGN=MIDDLE  ALT=\"+f%28g%28x%29%29+=+%28sqrt%282x%29+%2B+4%29%28sqrt%282x%29+%2B+4%29+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28g%28x%29%29+=+%28sqrt%282x%29%29%5E2+%2B+8sqrt%282x%29+%2B+16+-+4+ ALIGN=MIDDLE  ALT=\"+f%28g%28x%29%29+=+%28sqrt%282x%29%29%5E2+%2B+8sqrt%282x%29+%2B+16+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- Used FOIL\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28g%28x%29%29+=+2x+%2B+8sqrt%282x%29+%2B+12+ ALIGN=MIDDLE  ALT=\"+f%28g%28x%29%29+=+2x+%2B+8sqrt%282x%29+%2B+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- Simplified.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, what's the domain of f(g(x)) in that case? It would be all real numbers x greater than or equal to zero. You can't plug in negative numbers into that function because doing so will force the 2x inside <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8sqrt%282x%29+ ALIGN=MIDDLE  ALT=\"+8sqrt%282x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to be a negative number, which you can't do inside square roots. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );