document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72616>Question 72616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve h(f(6))\r<BR>\n" );
document.write( "\n" );
document.write( "if <BR>\n" );
document.write( "h(x)= -x^2 + 6x<BR>\n" );
document.write( "f(x)= 7x - 40 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51915 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all find f(6) by going to the original definition for f(x) and then replacing every<BR>\n" );
document.write( "x by 6 and then simplifying the result.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You were given that <BR>\n" );
document.write( ".<BR>\n" );
document.write( "f(x) = 7*x - 40<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then to find f(6) you replace every x in the equation for f(x) by 6 to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "f(6) = 7*6 - 40<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And you simplify the right side to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "f(6) = 42 - 40 = 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So now you know that f(6) = 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next you are asked to find h(f(6)) given that <BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29+=+-x%5E2+%2B+6x ALIGN=MIDDLE  ALT=\"h%28x%29+=+-x%5E2+%2B+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "To find h(f(6)) you just replace every x in h(x) with f(6). The result would be:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28f%286%29%29+=+-%28f%286%29%29%5E2+%2B+6%2A%28f%286%29%29 ALIGN=MIDDLE  ALT=\"h%28f%286%29%29+=+-%28f%286%29%29%5E2+%2B+6%2A%28f%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "But on the right side you can substitute for f(6) its value which we found to be +2.  If <BR>\n" );
document.write( "you do your equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28f%286%29%29+=+-%282%29%5E2+%2B+6%2A2 ALIGN=MIDDLE  ALT=\"h%28f%286%29%29+=+-%282%29%5E2+%2B+6%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and the right side simplifies to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28f%286%29%29+=+-4+%2B+12+=+8 ALIGN=MIDDLE  ALT=\"h%28f%286%29%29+=+-4+%2B+12+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the answer to your problem is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28f%286%29%29+=+8 ALIGN=MIDDLE  ALT=\"h%28f%286%29%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to better understand the way to work problems such as these. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );