document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176999>Question 176999</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain and range of this function f(x)=1/squareroot of (x-4)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132053 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=132053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The domain is all of the x values that make f(x) defined. <BR>\n" );
document.write( "There are two restrictions on the domain to be concerned about. <BR>\n" );
document.write( "First, the square root can only have zero or positive values as arguments, because the square root of a negative number is undefined. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4%3C0 ALIGN=MIDDLE  ALT=\"x-4%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C4 ALIGN=MIDDLE  ALT=\"x%3C4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Second, since it's a fraction, the denominator cannot be zero because division by zero is undefined. <BR>\n" );
document.write( "Find the point(s) where the denominator equals zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=0 ALIGN=MIDDLE  ALT=\"x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If we put the two together, x cannot be less than 4 and x cannot be equal to 4. <BR>\n" );
document.write( "Therefore the domain is x such that x is greater than 4.<BR>\n" );
document.write( "Domain:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "To get the range look at the domain. <BR>\n" );
document.write( "Near x gets close to 4 (say 4.001), the denominator gets very small, the value of f(x) gets zero large.<BR>\n" );
document.write( "As x gets very larger, the denominator gets very large, the value of f(x) goes towards 0.<BR>\n" );
document.write( "Range:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >) </SPAN>\n" );
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