document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242808>Question 242808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain and range of the INVERSE of the given function.<BR>\n" );
document.write( "Square root x-3<BR>\n" );
document.write( "I think the answer is Domain [0,infenity), Range [3,0) or the answer might be Domain: all real numbers; range [3,infenity).   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177775 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=177775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=sqrt%28x-3%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=sqrt%28x-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there is a restriction on the values of x (Domain!), because of the square root operation.  Whatever is INSIDE the square root (this is called the RADICAND!), must be greater than or equal to zero.\r<BR>\n" );
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document.write( "So, Domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3%3E=0 ALIGN=MIDDLE  ALT=\"x-3%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=3 ALIGN=MIDDLE  ALT=\"x%3E=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, the Range is the set of all resulting y values. Because y = a square root, y cannot be negative.  Also, the values of y increase without bound, so the <BR>\n" );
document.write( "Range is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=0 ALIGN=MIDDLE  ALT=\"y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What we just determined was the DOMAIN and RANGE of the FUNCTION.  Now, for the INVERSE FUNCTION, DOMAIN and RANGE are REVERSED!\r<BR>\n" );
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document.write( "For the INVERSE FUNCTION, Domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or [0, inf),<BR>\n" );
document.write( "and Range is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=3 ALIGN=MIDDLE  ALT=\"y%3E=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or [3, inf).\r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Seminole State College of Florida<BR>\n" );
document.write( "Altamonte Springs Campus </SPAN>\n" );
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