document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=942368>Question 942368</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the function h whose domain is the interval<BR>\n" );
document.write( "[&#8722;3, 3], with h defined on this domain by the formula<BR>\n" );
document.write( "h(x) = (3 + x)^2.<BR>\n" );
document.write( "Does h have an inverse? If so, find it, along with its<BR>\n" );
document.write( "domain and range. If not, explain why not. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #574493 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=574493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In that domain, h has an inverse.  h takes a value at -3 and up to 3 for x.  The interval of h [-3, 0] gets an inverse but the interval [0, 3] gets a different inverse.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B3%29%5E2=x ALIGN=MIDDLE  ALT=\"%28y%2B3%29%5E2=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3=0%2B-+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y%2B3=0%2B-+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%2B-+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y=-3%2B-+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------the inverse relation, TWO branches.\r<BR>\n" );
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document.write( "The left branch of h has the inverse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3-sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y=-3-sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "domain of y [0, 9] and range from -3 to 0 or [-3, 0].<BR>\n" );
document.write( "Notice how the domain and range for h become switched in the inverse.\r<BR>\n" );
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document.write( "Similar happens with the other branch.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-7%2C7%2C-7%2C7%2C-3-sqrt%28x%29%2C-3%2Bsqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-7%2C7%2C-7%2C7%2C-3-sqrt%28x%29%2C-3%2Bsqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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