document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201999>Question 1201999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x) = 2x, g(x) = x—5, and h(x)=x^2-1. Find each value.\r<BR>\n" );
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document.write( "(1) (fh)(2)<BR>\n" );
document.write( "(2) (gh)(-2)<BR>\n" );
document.write( "(3) (f/h)<BR>\n" );
document.write( "(4) (h/g)(0)<BR>\n" );
document.write( "(5) (g/f)(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836607 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=836607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Normally I would point out that the rule of this website is \"one question per post\". \r<BR>\n" );
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document.write( "However, these questions are fairly short so it's not the end of the world to have them all together like this.\r<BR>\n" );
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document.write( "====================================================================================\r<BR>\n" );
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document.write( "Problem 1\r<BR>\n" );
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document.write( "Method 1<BR>\n" );
document.write( "f(x) = 2x<BR>\n" );
document.write( "f(2) = 2*2<BR>\n" );
document.write( "f(2) = 4<BR>\n" );
document.write( "and<BR>\n" );
document.write( "h(x) = x^2-1<BR>\n" );
document.write( "h(2) = 2^2-1<BR>\n" );
document.write( "h(2) = 4-1<BR>\n" );
document.write( "h(2) = 3<BR>\n" );
document.write( "those results lead to<BR>\n" );
document.write( "(fh)(2) = f(2)*h(2)<BR>\n" );
document.write( "(fh)(2) = 4*3<BR>\n" );
document.write( "(fh)(2) = 12\r<BR>\n" );
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document.write( "Method 2<BR>\n" );
document.write( "(fh)(x) = f(x)*h(x)<BR>\n" );
document.write( "(fh)(x) = ( f(x) )*( h(x) )<BR>\n" );
document.write( "(fh)(x) = ( 2x )*( x^2-1 )<BR>\n" );
document.write( "(fh)(x) = 2x^3-2x<BR>\n" );
document.write( "(fh)(2) = 2*2^3-2*2<BR>\n" );
document.write( "(fh)(2) = 2*8-4<BR>\n" );
document.write( "(fh)(2) = 16-4<BR>\n" );
document.write( "(fh)(2) = 12\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>12</font>\r<BR>\n" );
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document.write( "Problem 2\r<BR>\n" );
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document.write( "Method 1<BR>\n" );
document.write( "g(x) = x-5<BR>\n" );
document.write( "g(-2) = -2-5<BR>\n" );
document.write( "g(-2) = -7<BR>\n" );
document.write( "and<BR>\n" );
document.write( "h(x) = x^2-1<BR>\n" );
document.write( "h(-2) = (-2)^2-1<BR>\n" );
document.write( "h(-2) = 4-1<BR>\n" );
document.write( "h(-2) = 3<BR>\n" );
document.write( "so,<BR>\n" );
document.write( "(gh)(-2) = g(-2)*h(-2)<BR>\n" );
document.write( "(gh)(-2) = -7*3<BR>\n" );
document.write( "(gh)(-2) = -21\r<BR>\n" );
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document.write( "Method 2<BR>\n" );
document.write( "(gh)(x) = g(x)*h(x)<BR>\n" );
document.write( "(gh)(x) = ( g(x) ) * ( h(x) )<BR>\n" );
document.write( "(gh)(x) = ( x-5 ) * ( x^2-1 )<BR>\n" );
document.write( "(gh)(x) = x( x^2-1 ) - 5( x^2-1 )<BR>\n" );
document.write( "(gh)(x) = x^3-x -5x^2+5 <BR>\n" );
document.write( "(gh)(x) = x^3-5x^2-x+5 <BR>\n" );
document.write( "(gh)(-2) = (-2)^3-5(-2)^2-(-2)+5 <BR>\n" );
document.write( "(gh)(-2) = -8-5*(4)+2+5 <BR>\n" );
document.write( "(gh)(-2) = -8-20+2+5<BR>\n" );
document.write( "(gh)(-2) = -21\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>-21</font>\r<BR>\n" );
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document.write( "Problem 3\r<BR>\n" );
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document.write( "f(x) = 2x<BR>\n" );
document.write( "h(x) = x^2 - 1<BR>\n" );
document.write( "(f/h) = f(x)/h(x)<BR>\n" );
document.write( "(f/h) = ( f(x) )/( h(x) )<BR>\n" );
document.write( "(f/h) = (2x)/(x^2-1)\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>(2x)/(x^2-1)</font>\r<BR>\n" );
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document.write( "Problem 4\r<BR>\n" );
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document.write( "Method 1<BR>\n" );
document.write( "h(x) = x^2-1<BR>\n" );
document.write( "h(0) = 0^2-1<BR>\n" );
document.write( "h(0) = 0-1<BR>\n" );
document.write( "h(0) = -1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "g(x) = x-5<BR>\n" );
document.write( "g(0) = 0-5<BR>\n" );
document.write( "g(0) = -5<BR>\n" );
document.write( "therefore,<BR>\n" );
document.write( "(h/g)(x) = ( h(x) )/( g(x) )<BR>\n" );
document.write( "(h/g)(0) = ( h(0) )/( g(0) )<BR>\n" );
document.write( "(h/g)(0) = ( -1 )/( -5 )<BR>\n" );
document.write( "(h/g)(0) = 1/5\r<BR>\n" );
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document.write( "Method 2<BR>\n" );
document.write( "(h/g)(x) = ( h(x) )/( g(x) )<BR>\n" );
document.write( "(h/g)(x) = ( x^2-1 )/( x-5 )<BR>\n" );
document.write( "(h/g)(0) = ( 0^2-1 )/( 0-5 )<BR>\n" );
document.write( "(h/g)(0) = ( -1 )/( -5 )<BR>\n" );
document.write( "(h/g)(0) = 1/5\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>1/5</font>\r<BR>\n" );
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document.write( "Problem 5\r<BR>\n" );
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document.write( "g(x) = x-5<BR>\n" );
document.write( "f(x) = 2x<BR>\n" );
document.write( "(g/f)(x) = ( g(x) )/( f(x) )<BR>\n" );
document.write( "(g/f)(x) = ( x-5 )/( 2x )\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>( x-5 )/( 2x )</font>\r<BR>\n" );
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document.write( "Summary:<ol><li><font color=red size=4>12</font></li><li><font color=red size=4>-21</font></li><li><font color=red size=4>(2x)/(x^2-1)</font></li><li><font color=red size=4>1/5</font></li><li><font color=red size=4>( x-5 )/( 2x )</font></li></ol><BR>\n" );
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