document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=58693>Question 58693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x)=x^2+3x-5,g(x)=x-3, find\r<BR>\n" );
document.write( "\n" );
document.write( "a. (f+g)(x)<BR>\n" );
document.write( "b. (f-g)(x)<BR>\n" );
document.write( "c. (fg)(x)<BR>\n" );
document.write( "d. (f/g)(x)<BR>\n" );
document.write( "e.(f of g)(x)<BR>\n" );
document.write( "f. g[f(x)]<BR>\n" );
document.write( "g.(f-g)(-2)<BR>\n" );
document.write( "h. f[f(3)]<BR>\n" );
document.write( "Please help!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40231 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=40231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let f(x)=x^2+3x-5,g(x)=x-3, find\r<BR>\n" );
document.write( "\n" );
document.write( "a. (f+g)(x)=(x^2+3x-5)+(x-3)<BR>\n" );
document.write( "(f+g)(x)=x^2+3x+x-5-3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28f%2Bg%29%28x%29=x%5E2%2B4x-8%29 ALIGN=MIDDLE  ALT=\"highlight%28%28f%2Bg%29%28x%29=x%5E2%2B4x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "b. (f-g)(x)=(x^2+3x-5)-(x-3)<BR>\n" );
document.write( "(f-g)(x)=x^2+3x-5-x+3<BR>\n" );
document.write( "(f-g)(x)=x^2+3x-x-5+3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28f-g%29%28x%29=x%5E2%2B2x-2%29 ALIGN=MIDDLE  ALT=\"highlight%28%28f-g%29%28x%29=x%5E2%2B2x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "c. (fg)(x)=(x^2+3x-5)(x-3)<BR>\n" );
document.write( "(fg)(x)=x(x^2+3x-5)-3(x^2+3x-5)<BR>\n" );
document.write( "(fg)(x)=x^3+3x^2-5x-3x^2-9x+15<BR>\n" );
document.write( "(fg)(x)=x^3+3x^2-3x^2-5x-9x+15<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28fg%29%28x%29=x%5E3-14x%2B15%29 ALIGN=MIDDLE  ALT=\"highlight%28%28fg%29%28x%29=x%5E3-14x%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "d. (f/g)(x)=(x^2+3x-5)/(x-3)  Nothing cancels by factoring so you're done.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28f%2Fg%29%28x%29=%28x%5E2%2B3x-5%29%2F%28x-3%29%29 ALIGN=MIDDLE  ALT=\"highlight%28%28f%2Fg%29%28x%29=%28x%5E2%2B3x-5%29%2F%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "e.(f of g)(x)=f(g(x))=f(x-3)  substitute x-3 in for x in f:<BR>\n" );
document.write( "(fog)(x)=(x-3)^2+3(x-3)-5<BR>\n" );
document.write( "(fog)(x)=x^2-6x+9+3x-9-5<BR>\n" );
document.write( "(fog)(x)=x^2-6x+3x+9-9-5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28fog%29%28x%29=x%5E2-3x-5%29 ALIGN=MIDDLE  ALT=\"highlight%28%28fog%29%28x%29=x%5E2-3x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "f. g[f(x)]=g(x^2+3x-5)  substitute x^2+3x-5 in for x in g<BR>\n" );
document.write( "g(f(x))=(x^2+3x-5)-3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28g%28f%28x%29%29=x%5E2%2B3x-8%29 ALIGN=MIDDLE  ALT=\"highlight%28g%28f%28x%29%29=x%5E2%2B3x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "g.(f-g)(-2) Take your answer from b and substitute -2 in for x.<BR>\n" );
document.write( "(f-g)(x)=x^2+2x-2<BR>\n" );
document.write( "(f-g)(-2)=(-2)^2+2(-2)-2<BR>\n" );
document.write( "(f-g)(-2)=4-4-2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28f-g%29%28-2%29=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28%28f-g%29%28-2%29=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":\r<BR>\n" );
document.write( "\n" );
document.write( "h. f[f(3)]<BR>\n" );
document.write( "Find f(3), f(3)=(3)^2+3(3)-5=9+9-5=13<BR>\n" );
document.write( "f(f(3))=f(13)<BR>\n" );
document.write( "f(f(3))=(13)^2+3(13)-5<BR>\n" );
document.write( "f(f(3))=169+39-5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28f%283%29%29=203%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28f%283%29%29=203%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );