document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201983>Question 1201983</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.<BR>\n" );
document.write( "(1) (f+g)(3)  <BR>\n" );
document.write( "(2) (f-h)(-1)  <BR>\n" );
document.write( "(3) (h-g)(x)  <BR>\n" );
document.write( "(4) (fg)(x)  <BR>\n" );
document.write( "(5) (fh)(2)  <BR>\n" );
document.write( "(6) (gh)(-2)<BR>\n" );
document.write( "(7) (f/h)  <BR>\n" );
document.write( "(8) (h/g)(0)  <BR>\n" );
document.write( "(9) (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 #836590 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=836590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The rule of this website is to post <b><u>one</u></b> problem at a time.\r<BR>\n" );
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document.write( "I'll do questions (1) through (4) to get you started.\r<BR>\n" );
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document.write( "Problem 1\r<BR>\n" );
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document.write( "f(x) = 2x<BR>\n" );
document.write( "f(3) = 2*3<BR>\n" );
document.write( "f(3) = 6<BR>\n" );
document.write( "and<BR>\n" );
document.write( "g(x) = x-5<BR>\n" );
document.write( "g(3) = 3-5<BR>\n" );
document.write( "g(3) = -2<BR>\n" );
document.write( "Therefore,<BR>\n" );
document.write( "(f+g)(3) = f(3)+g(3) = 6 + (-2) = 4\r<BR>\n" );
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document.write( "Here's another approach:<BR>\n" );
document.write( "(f+g)(x) = f(x)+g(x)<BR>\n" );
document.write( "(f+g)(x) = ( 2x ) + ( x-5 )<BR>\n" );
document.write( "(f+g)(x) = 3x-5<BR>\n" );
document.write( "(f+g)(3) = 3*3-5<BR>\n" );
document.write( "(f+g)(3) = 9-5<BR>\n" );
document.write( "(f+g)(3) = 4\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>4</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( "f(x) = 2x<BR>\n" );
document.write( "f(-1) = 2*(-1)<BR>\n" );
document.write( "f(-1) = -2<BR>\n" );
document.write( "and<BR>\n" );
document.write( "h(x) = x^2-1<BR>\n" );
document.write( "h(-1) = (-1)^2-1<BR>\n" );
document.write( "h(-1) = 1-1<BR>\n" );
document.write( "h(-1) = 0<BR>\n" );
document.write( "Both of those lead to<BR>\n" );
document.write( "(f-h)(-1) = f(-1) - h(-1)<BR>\n" );
document.write( "(f-h)(-1) = -2 - 0<BR>\n" );
document.write( "(f-h)(-1) = -2\r<BR>\n" );
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document.write( "Method 2<BR>\n" );
document.write( "(f-h)(x) = f(x)-h(x)<BR>\n" );
document.write( "(f-h)(x) = (2x) - (x^2-1)<BR>\n" );
document.write( "(f-h)(x) = 2x - x^2+1<BR>\n" );
document.write( "(f-h)(x) = -x^2 + 2x + 1<BR>\n" );
document.write( "(f-h)(-1) = -(-1)^2 + 2(-1) + 1<BR>\n" );
document.write( "(f-h)(-1) = -(1) + 2(-1) + 1<BR>\n" );
document.write( "(f-h)(-1) = -1 - 2 + 1<BR>\n" );
document.write( "(f-h)(-1) = -3 + 1<BR>\n" );
document.write( "(f-h)(-1) = -2\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>-2</font>\r<BR>\n" );
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document.write( "Problem 3\r<BR>\n" );
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document.write( "(h-g)(x) = h(x) - g(x)<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)(x) =  x^2-1  -  x+5 <BR>\n" );
document.write( "(h-g)(x) =  x^2 - x + 4 \r<BR>\n" );
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document.write( "Answer: <font color=red size=4>x^2 - x + 4</font>\r<BR>\n" );
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document.write( "Problem 4\r<BR>\n" );
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document.write( "(fg)(x) = f(x)*g(x)<BR>\n" );
document.write( "(fg)(x) = [ f(x) ] * [ g(x) ]<BR>\n" );
document.write( "(fg)(x) = [ 2x ] * [ x-5 ]<BR>\n" );
document.write( "(fg)(x) = 2x(x-5)<BR>\n" );
document.write( "(fg)(x) = 2x*x + 2x*(-5)<BR>\n" );
document.write( "(fg)(x) = 2x^2 - 10x\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>2x^2 - 10x</font><BR>\n" );
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