document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214823>Question 214823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I seem to have a problem with functions!\r<BR>\n" );
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document.write( "n(x)=3^x     m(t)=SQRT(t)+1      find m(n(x))\r<BR>\n" );
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document.write( "My solution was SQRT(3^x)+1.\r<BR>\n" );
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document.write( "Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162299 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=162299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> n(x) = 3^x<BR>\n" );
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document.write( "m(t) = sqrt(t) + 1<BR>\n" );
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document.write( "find m(n(x))<BR>\n" );
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document.write( "substitute n(x) for t in the equation of m(t).<BR>\n" );
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document.write( "since n(x) = 3^x, this means that:<BR>\n" );
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document.write( "m(t) = sqrt(t) + 1 becomes:<BR>\n" );
document.write( "m(3^x) = sqrt(3^x) + 1<BR>\n" );
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document.write( "that should be your equation.<BR>\n" );
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document.write( "to prove this is true, substitute any value for x and solve.<BR>\n" );
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document.write( "let x = 8 (chosen at random)<BR>\n" );
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document.write( "n(x) = 3^x = 3^8 = 6561<BR>\n" );
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document.write( "m(3^x) = sqrt(3^x) + 1 = sqrt(3^8)) + 1 = sqrt(6561) + 1 = 81 + 1 = 82<BR>\n" );
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document.write( "m(t) = sqrt(t) + 1<BR>\n" );
document.write( "let t = 6561<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "m(t) = sqrt(t) + 1 = sqrt(6561) + 1 = 81 + 1 = 82<BR>\n" );
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document.write( "you get the same answer whether you solve for:<BR>\n" );
document.write( "m(n(x)) = sqrt(n(x)) + 1 directly, or whether you solve for:<BR>\n" );
document.write( "n(x) first and then use that value in m(t).<BR>\n" );
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document.write( "the equations are equivalent.<BR>\n" );
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document.write( "the key to solving these types of problems is to substitute the function for the variable and then solve.<BR>\n" );
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document.write( "check this website out.<BR>\n" );
document.write( "It has some examples that may help you to understand what is going on.<BR>\n" );
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document.write( "http://www.regentsprep.org/Regents/math/algtrig/ATP5/EvaluatingFunctions.htm<BR>\n" );
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document.write( "just copy that line into your browser address bar and hit the return.<BR>\n" );
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document.write( "it's short and sweet so take the time to look at it if you can.<BR>\n" );
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document.write( "fyi,<BR>\n" );
document.write( "your solution was correct.<BR>\n" );
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