document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161482>Question 161482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM PLEASE:\r<BR>\n" );
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document.write( "Find the domain of the composite function f o g.\r<BR>\n" );
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document.write( "f(x) = 2 / x + 10 , g(x) = 60 / x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118993 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=118993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = 2/x + 10<BR>\n" );
document.write( "i'll assume that means (2/x) + 10.<BR>\n" );
document.write( "hopefully that's right.<BR>\n" );
document.write( "if not, resubmit the question.<BR>\n" );
document.write( "g(x) = 60/x.<BR>\n" );
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document.write( "i assume you are looking for f(g(x)).<BR>\n" );
document.write( "if that's what fog means then we're ok.<BR>\n" );
document.write( "i'll answer for that.<BR>\n" );
document.write( "resubmit the question if i got it wrong.<BR>\n" );
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document.write( "g(x) = 60/x (given)<BR>\n" );
document.write( "f(x) = (2/x) + 10 (given)<BR>\n" );
document.write( "to solve for f(g(x)) you have to replace x with g(x).<BR>\n" );
document.write( "this is no different then solving for f(3).<BR>\n" );
document.write( "you replace x with 3.<BR>\n" );
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document.write( "in this case you replace x with g(x) which means you replace<BR>\n" );
document.write( "x with (60/x)<BR>\n" );
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document.write( "since f(x) = (2/x) + 10, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29+=+f%28%2860%2Fx%29%29+=+%28%282%29%2F%2860%2Fx%29%29+%2B+10 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29+=+f%28%2860%2Fx%29%29+=+%28%282%29%2F%2860%2Fx%29%29+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2/(60/x) is the same as (2*x)/60.<BR>\n" );
document.write( "you get that by multiplying the numerator and denominator by x.<BR>\n" );
document.write( "2*x/(60*x/x) = 2*x/60 since the x in the denominator cancels out.<BR>\n" );
document.write( "equation becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29+=+f%28%2860%2Fx%29%29+=+%282%2Ax%2F%2860%29%29+%2B+10 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29+=+f%28%2860%2Fx%29%29+=+%282%2Ax%2F%2860%29%29+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29+=+f%28%2860%2Fx%29%29+=+%28x%2F30%29+%2B+10 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29+=+f%28%2860%2Fx%29%29+=+%28x%2F30%29+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the domain of f(x) would be all values of x except 0 since you can't divide by 0.<BR>\n" );
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document.write( "the domain of g(x) would be the same, i.e. all values of x except 0 for the same reason.<BR>\n" );
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document.write( "the domain of f(g(x)), however, would be all values of x since x is now in the numerator rather than the denominator.<BR>\n" );
document.write( " </SPAN>\n" );
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