document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=960391>Question 960391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For f(x)=(3x^2)+5and g(x)=7x-2,\r<BR>\n" );
document.write( "\n" );
document.write( "a. Verify: g(x + 2) &#8800; g(x) + g(2).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b. Find (f – g)(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c. Using the resulting function in (b), show that (f – g)(2) = f(2) – g(2).<BR>\n" );
document.write( "(The work should be different for each side of the equation.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d. Is (fg)(0) =(f/g)(0)? Explain.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "e. Find (f(x+h)-f(x))/h , h &#8800; 0.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #586941 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=586941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x%5E2%2B5 ALIGN=MIDDLE  ALT=\"f%28x%29=3x%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=7x-2 ALIGN=MIDDLE  ALT=\"g%28x%29=7x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a. Verify:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x+%2B+2%29+%3C%3Eg%28x%29+%2B+g%282%29 ALIGN=MIDDLE  ALT=\"g%28x+%2B+2%29+%3C%3Eg%28x%29+%2B+g%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "first find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%2B2%29 ALIGN=MIDDLE  ALT=\"g%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%2B2%29=7%28x%2B2%29-2 ALIGN=MIDDLE  ALT=\"g%28x%2B2%29=7%28x%2B2%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%2B2%29=7x%2B14-2 ALIGN=MIDDLE  ALT=\"g%28x%2B2%29=7x%2B14-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%2B2%29=7x%2B12 ALIGN=MIDDLE  ALT=\"g%28x%2B2%29=7x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%282%29 ALIGN=MIDDLE  ALT=\"g%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%282%29=7%282%29-2 ALIGN=MIDDLE  ALT=\"g%282%29=7%282%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%282%29=14-2 ALIGN=MIDDLE  ALT=\"g%282%29=14-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%282%29=12 ALIGN=MIDDLE  ALT=\"g%282%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "substitute it in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x+%2B+2%29+%3C%3E+g%28x%29+%2B+g%282%29 ALIGN=MIDDLE  ALT=\"g%28x+%2B+2%29+%3C%3E+g%28x%29+%2B+g%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B12+%3C%3E7x%2B12+%2B+12 ALIGN=MIDDLE  ALT=\"7x%2B12+%3C%3E7x%2B12+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B12+%3C%3E7x%2B24 ALIGN=MIDDLE  ALT=\"7x%2B12+%3C%3E7x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b. Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f-g%29%28x%29+ ALIGN=MIDDLE  ALT=\"%28f-g%29%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f-g%29%28x%29+=f%28x%29+-g%28x%29+ ALIGN=MIDDLE  ALT=\"%28f-g%29%28x%29+=f%28x%29+-g%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f-g%29%28x%29+=3x%5E2%2B5+-%287x-2%29+ ALIGN=MIDDLE  ALT=\"%28f-g%29%28x%29+=3x%5E2%2B5+-%287x-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f-g%29%28x%29+=3x%5E2%2B5+-7x%2B2 ALIGN=MIDDLE  ALT=\"%28f-g%29%28x%29+=3x%5E2%2B5+-7x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f-g%29%28x%29+=3x%5E2+-7x%2B7 ALIGN=MIDDLE  ALT=\"%28f-g%29%28x%29+=3x%5E2+-7x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c. Using the resulting function in (b), show that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f-g%29%282%29+=+f%282%29-g%282%29 ALIGN=MIDDLE  ALT=\"%28f-g%29%282%29+=+f%282%29-g%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "(The work should be different for each side of the equation.)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f-g%29%28x%29+=+f%282%29+%96+g%282%29 ALIGN=MIDDLE  ALT=\"%28f-g%29%28x%29+=+f%282%29+%96+g%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A2%5E2+-7%2A2%2B7=+3%2A2%5E2%2B5+-%287%2A2-2%29+ ALIGN=MIDDLE  ALT=\"3%2A2%5E2+-7%2A2%2B7=+3%2A2%5E2%2B5+-%287%2A2-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A4+-14%2B7=+3%2A4%2B5+-%2814-2%29+ ALIGN=MIDDLE  ALT=\"3%2A4+-14%2B7=+3%2A4%2B5+-%2814-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+-7=+12%2B5+-%2812%29+ ALIGN=MIDDLE  ALT=\"12+-7=+12%2B5+-%2812%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=+17+-12+ ALIGN=MIDDLE  ALT=\"5=+17+-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=+5 ALIGN=MIDDLE  ALT=\"5=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d. Is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28fg%29%280%29+=%28f%2Fg%29%280%29 ALIGN=MIDDLE  ALT=\"%28fg%29%280%29+=%28f%2Fg%29%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >? Explain.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28fg%29%280%29+=%28f%2Fg%29%280%29 ALIGN=MIDDLE  ALT=\"%28fg%29%280%29+=%28f%2Fg%29%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2%2B5%29%287x-2%29+=%283x%5E2%2B5%29%2F%287x-2%29+ ALIGN=MIDDLE  ALT=\"%283x%5E2%2B5%29%287x-2%29+=%283x%5E2%2B5%29%2F%287x-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A0%5E2%2B5%29%287%2A0-2%29+=%283%2A0%5E2%2B5%29%2F%287%2A0-2%29 ALIGN=MIDDLE  ALT=\"%283%2A0%5E2%2B5%29%287%2A0-2%29+=%283%2A0%5E2%2B5%29%2F%287%2A0-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%28-2%29+=%285%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"%285%29%28-2%29+=%285%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10+%3C%3E-5%2F2+ ALIGN=MIDDLE  ALT=\"-10+%3C%3E-5%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....so, the product (on the left side of equation) could not be same as the quotient (on the right side of equation)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "e. Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%2Bh%29-f%28x%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+%3C%3E+0 ALIGN=MIDDLE  ALT=\"h+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%2Bh%29-f%28x%29%29%2Fh=%283%28x%2Bh%29%5E2%2B5-%283x%5E2%2B5%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh=%283%28x%2Bh%29%5E2%2B5-%283x%5E2%2B5%29%29%2Fh\"   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=%28f%28x%2Bh%29-f%28x%29%29%2Fh=%283%28x%5E2%2B2hx%2Bh%5E2%29%2Bcross%285%29-3x%5E2-cross%285%29%29%2Fh 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=%28f%28x%2Bh%29-f%28x%29%29%2Fh=%28cross%283x%5E2%29%2B6hx%2B3h%5E2-cross%283x%5E2%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh=%28cross%283x%5E2%29%2B6hx%2B3h%5E2-cross%283x%5E2%29%29%2Fh\"   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=%28f%28x%2Bh%29-f%28x%29%29%2Fh=%286hx%2B3h%5E2%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh=%286hx%2B3h%5E2%29%2Fh\"   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=%28f%28x%2Bh%29-f%28x%29%29%2Fh=3cross%28h%29%282x%2Bh%29%29%2Fcross%28h%29 ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh=3cross%28h%29%282x%2Bh%29%29%2Fcross%28h%29\"   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=%28f%28x%2Bh%29-f%28x%29%29%2Fh=3%282x%2Bh%29 ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh=3%282x%2Bh%29\"   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=%28f%28x%2Bh%29-f%28x%29%29%2Fh=6x%2B3h ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh=6x%2B3h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );