document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=410515>Question 410515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=5x-4 and g(x)=x^2+3. Find the following:<BR>\n" );
document.write( "(g-f)(x)<BR>\n" );
document.write( "(fg)(x)<BR>\n" );
document.write( "domain of g/f </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288634 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=288634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (g-f)(x)<BR>\n" );
document.write( "= g(x) - f(x) <BR>\n" );
document.write( "= (x^2 + 3) - (5x - 4) <BR>\n" );
document.write( "= x^2 + 3 - 5x + 4<BR>\n" );
document.write( "= x^2 - 5x + 7\r<BR>\n" );
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document.write( "(fg)(x)<BR>\n" );
document.write( "= f(x) * g(x)<BR>\n" );
document.write( "= (5x-4) * (x^2 + 3)<BR>\n" );
document.write( "= 5x^3 + 15x - 4x^2 - 12<BR>\n" );
document.write( "= 5x^3 - 4x^2 + 15x - 12\r<BR>\n" );
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document.write( "(g/f)(x)<BR>\n" );
document.write( "= g(x) / f(x)<BR>\n" );
document.write( "= (x^2 + 3) / (5x-4)<BR>\n" );
document.write( "the denominator = 0 when 5x-4 = 0<BR>\n" );
document.write( "this occurs when x = 4/5<BR>\n" );
document.write( "the function is undefined when the denominator is equal to 0<BR>\n" );
document.write( "the domain is therefore all real values of x except when x = 4/5\r<BR>\n" );
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document.write( "the graph of this equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-5%2C5%2C%28x%5E2%2B3%29+%2F+%285x-4%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-5%2C5%2C%28x%5E2%2B3%29+%2F+%285x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if you draw a vertical line at x = 4/5, you will see that the graph of the function approaches that line but never touches it.  that means that the line x = 4/5 is an asymptote of the function which also means that that the function is undefined at x = 4/5.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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