document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256549>Question 256549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please do a step by step informative answer for the following question? I am having to take a placement test and cannot for the life of me remember how to perform a function!!!  Thanks!<BR>\n" );
document.write( "The whole question goes as follows:<BR>\n" );
document.write( "Listed below are 5 functions< each denoted g(x) and each involving a real number constant c>1. <BR>\n" );
document.write( "If f(x)=2 to the x, which of these 5 functions yeilds the greatest value for<BR>\n" );
document.write( "f(g(x)), for all x>1?<BR>\n" );
document.write( "a. g(x)=cx<BR>\n" );
document.write( "b. g(x)=c/x<BR>\n" );
document.write( "c. g(x)=x/c<BR>\n" );
document.write( "d. g(x)=x-c<BR>\n" );
document.write( "e. g(x)=logsubscriptc x\r<BR>\n" );
document.write( "\n" );
document.write( "HELP! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188656 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=188656\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) f(g(x)) will become 2^cx. As x increases f(g(x)) increases<BR>\n" );
document.write( "(b) f(g(x)) will become 2^c/x. As x increases f(g(x)) decreases<BR>\n" );
document.write( "(c) f(g(x)) will become 2^x/c. As x increases f(g(x)) increases<BR>\n" );
document.write( "(d) f(g(x)) will become 2^(x-c). As x increases f(g(x)) increases<BR>\n" );
document.write( "(e) f(g(x)) will become 2^(log_c(x)). As x increases f(g(x)) increases<BR>\n" );
document.write( "--<BR>\n" );
document.write( "Now (b) decreases, so it is out of contention.<BR>\n" );
document.write( "Since c is a constant, let c = 3. We get<BR>\n" );
document.write( "--<BR>\n" );
document.write( "(a) f(g(x)) will become 2^(3x). As x increases f(g(x)) increases<BR>\n" );
document.write( "(c) f(g(x)) will become 2^(x/3). As x increases f(g(x)) increases<BR>\n" );
document.write( "(d) f(g(x)) will become 2^(x-3). As x increases f(g(x)) increases<BR>\n" );
document.write( "(e) f(g(x)) will become 2^(log_c(x)). As x increases f(g(x)) increases<BR>\n" );
document.write( "Now, (c) < (a), so (c) is out. (d) < (a) so (d) is out. We now have:<BR>\n" );
document.write( "--<BR>\n" );
document.write( "(a) f(g(x)) will become 2^(3x). As x increases f(g(x)) increases<BR>\n" );
document.write( "(e) f(g(x)) will become 2^(log_c(x)). As x increases f(g(x)) increases<BR>\n" );
document.write( "--<BR>\n" );
document.write( "It turns out that (a) grows a lot faster than (e) so (a) is the largest value. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );