document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=633882>Question 633882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The domain of the function f is {x: -1 < x < 5}. If g(x) = 2f(-x), what is the domain of the function g?\r<BR>\n" );
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document.write( "i know that the answer is (-5 < x < 1) but I am curious about the steps necessary to get that answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #399313 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=399313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For x such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%3Cx%3C1 ALIGN=MIDDLE  ALT=\"-5%3Cx%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%3E-x%3E-1 ALIGN=MIDDLE  ALT=\"5%3E-x%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3C-x%3C5 ALIGN=MIDDLE  ALT=\"-1%3C-x%3C5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so (-x) is in the domain of f(x).<BR>\n" );
document.write( "Therefore, f(-x) is defined, and can be calculated and multiplied times 2 to find g(x).<BR>\n" );
document.write( "For example, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-4%29=2%2Af%284%29 ALIGN=MIDDLE  ALT=\"g%28-4%29=2%2Af%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > exists, and so does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%280.7%29=2%2Af%28-0.7%29 ALIGN=MIDDLE  ALT=\"g%280.7%29=2%2Af%28-0.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "On the other hand, when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-5 ALIGN=MIDDLE  ALT=\"x%3C=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%3E=5 ALIGN=MIDDLE  ALT=\"-x%3E=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,and<BR>\n" );
document.write( "(-x) is out of the domain of f(x).<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=1 ALIGN=MIDDLE  ALT=\"x%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%3C=-1 ALIGN=MIDDLE  ALT=\"-x%3C=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is outside the domain of f(x).<BR>\n" );
document.write( "In either case case f(-x) does not exist, and neither does g(x).<BR>\n" );
document.write( "For example for x=-5, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-5%29=2%2Af%285%29 ALIGN=MIDDLE  ALT=\"g%28-5%29=2%2Af%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not exist. It is not defined.<BR>\n" );
document.write( "The same goes for x=1. In that case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%281%29=2%2Af%28-1%29 ALIGN=MIDDLE  ALT=\"g%281%29=2%2Af%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not exist either.<BR>\n" );
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document.write( "The function f(x) could be simply defined as f(x)=8 for x such that -1<x<5 (not defined for any other x).<BR>\n" );
document.write( "If you like a fancier function, an example could be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2Fsqrt%28%28x%2B1%29%285-x%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2Fsqrt%28%28x%2B1%29%285-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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