document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031448>Question 1031448</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Range of function f(x)=1/(2-cos3x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646125 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=646125\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is a fact that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C=+cos3x+%3C=+1 ALIGN=MIDDLE  ALT=\"-1+%3C=+cos3x+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real values x.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3E=+-cos3x+%3E=+-1 ALIGN=MIDDLE  ALT=\"1+%3E=+-cos3x+%3E=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%3E=+2-cos3x+%3E=+1 ALIGN=MIDDLE  ALT=\"3+%3E=+2-cos3x+%3E=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after adding 2 to all sides..<BR>\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3+%3C=+1%2F%282-cos3x%29+%3C=+1 ALIGN=MIDDLE  ALT=\"1%2F3+%3C=+1%2F%282-cos3x%29+%3C=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after inversion (notice that all terms are positive)\r<BR>\n" );
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document.write( "==> The range of f(x) is the closed interval [1/3, 1]. </SPAN>\n" );
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