document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202867>Question 202867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One of the tutors pleaseeee pleaseee help me with the following Advanced Functions question. I would be greatly thankful. \r<BR>\n" );
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document.write( "Given the functions f(x)=3^x, g(x)=x+2, and h(x)=2x-3, what composition of functions would result in each of the following?(3 marks:1 mark each)<BR>\n" );
document.write( "a)y=(2)*(3^x+2)-(3)<BR>\n" );
document.write( "b)y=3^2x+1<BR>\n" );
document.write( "c)y=(1/27)*(3^2x)+(2)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153034 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=153034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) =3^x,,,,,g(x) = (x+2),,,,,,h(x) = (2x-3)<BR>\n" );
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document.write( "(a) y= h[g{f(x)}] = h[{ (3^x) +2 }] = 2[3^x +2] -3 <BR>\n" );
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document.write( "(b) y = f[h{g(x)}] = f[ 2{x+2} -3]=f[2x+4-3] = f[2x+1] = 3^(2x+1)<BR>\n" );
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document.write( "(c) y= g[f{h(x)}]= g[3^{2x-3}]=[{3^(2x-3)} +2] ={3^2x-3^-3} +2 = <BR>\n" );
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document.write( "3^(2x)/3^3+2=1/27*3^(2x) +2<BR>\n" );
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