document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074223>Question 1074223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!  Thank you for your time.<BR>\n" );
document.write( "I am trying to solve a function problem and so far I haven't been able to find similar practice questions where two different functions are given.\r<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------------------------------<BR>\n" );
document.write( "If f(x)= 12 - (x^2 / 2) and f(2k) = 2k, what is one possible value of k? \r<BR>\n" );
document.write( "\n" );
document.write( "The multiple choice options are : 2 , 3, 4, 6, 8 <BR>\n" );
document.write( "----------------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "What I'm stuck on: if f(2k) = 2k, wouldn't that mean 2k = 2k, thus k = k? So any value can be inputted?  I'm not sure what I should do with x either...\r<BR>\n" );
document.write( "\n" );
document.write( "Any insight into how to go about solving a problem like this is very much appreciated! It's been a few years since I've worked with functions.  Thanks once again! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688931 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282k%29 ALIGN=MIDDLE  ALT=\"f%282k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number you get when you replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k ALIGN=MIDDLE  ALT=\"2k\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in the function (formula) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%22...%22 ALIGN=MIDDLE  ALT=\"f%28x%29=%22...%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > given.<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "The unexpected brackets add no meaning, but they do not hurt.<BR>\n" );
document.write( "They are unexpected because \"f(x)= 12 - (x^2 / 2) \".<BR>\n" );
document.write( "means the same as f(x) = 12 - x^2 /2 , or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+12+-+x%5E2+%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+12+-+x%5E2+%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "What the problem you posted says, in other words,<BR>\n" );
document.write( "is to solve the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-%28%282k%29%5E2%2F2%29=2k ALIGN=MIDDLE  ALT=\"12-%28%282k%29%5E2%2F2%29=2k\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or at least verify if one of the solutions given makes the equation true.<BR>\n" );
document.write( " <BR>\n" );
document.write( "This looks like a problem you may face in a timed test,<BR>\n" );
document.write( "so finding the most effective strategy will help.<BR>\n" );
document.write( "(I failed at strategy this time, but hindsight may help me next time).<BR>\n" );
document.write( " <BR>\n" );
document.write( "1) CHECKING THE CHOICES:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C6%2C%22k+=%22%2C2%2C3%2C4%2C6%2C8%2C%0D%0A%222+k+=%22%2C4%2C6%2C8%2C12%2C16%2C%0D%0A%22f+%28+2+k+%29+=%22%2C12-4%5E2%2F2=12-16%2F2=12-8%2C12-6%5E2%2F2%2Cnegative%2Cnegative%2Cnegative%2C%0D%0A%22+%22%2C%22=4%22%2C%22=12-36%2F2=12-18=-6%22%2Cnumber%2Cnumber%2Cnumber%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "2) SOLVING THE EQUATION:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-%282k%29%5E2%2F2=2k ALIGN=MIDDLE  ALT=\"12-%282k%29%5E2%2F2=2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-4k%5E2%2F2=2k ALIGN=MIDDLE  ALT=\"12-4k%5E2%2F2=2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-2k%5E2=2k ALIGN=MIDDLE  ALT=\"12-2k%5E2=2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From here, you may divide everything by 2 (or not),<BR>\n" );
document.write( "and solve the equation to find the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=2 ALIGN=MIDDLE  ALT=\"k=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-3 ALIGN=MIDDLE  ALT=\"k=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "3) THE OTHER OPTION:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2k ALIGN=MIDDLE  ALT=\"y=2k\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a change of variable, tells you to solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28y%29=y ALIGN=MIDDLE  ALT=\"f%28y%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-y%5E2%2F2=y ALIGN=MIDDLE  ALT=\"12-y%5E2%2F2=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You could solve, you could check y=4, 6, 8, 12, and 16.<BR>\n" );
document.write( "You could look at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-y%5E2%2F2=y ALIGN=MIDDLE  ALT=\"12-y%5E2%2F2=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-y=y%5E2%2F2 ALIGN=MIDDLE  ALT=\"12-y=y%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and decide that from the options given,<BR>\n" );
document.write( "the only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F2 ALIGN=MIDDLE  ALT=\"y%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > that will work is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2%2F2=16%2F2=8 ALIGN=MIDDLE  ALT=\"4%5E2%2F2=16%2F2=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because the other ones will yield too large a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F2%3E=6%5E2%2F2=36%2F2=18 ALIGN=MIDDLE  ALT=\"y%5E2%2F2%3E=6%5E2%2F2=36%2F2=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );