document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028867>Question 1028867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the inverse function of f:[3,&#8734;) -> R, f(x) = (x-4)^2 +1<BR>\n" );
document.write( "Why does the domain of f need to be restricted to [4,&#8734;) in this question? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643929 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=643929\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look first for the inverse relation to f.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%28x%29-4%29%5E2%2B1=x ALIGN=MIDDLE  ALT=\"%28R%28x%29-4%29%5E2%2B1=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the inverse function of f.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%28x%29-4%29%5E2=x-1 ALIGN=MIDDLE  ALT=\"%28R%28x%29-4%29%5E2=x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29-4=0%2B-+sqrt%28x-1%29 ALIGN=MIDDLE  ALT=\"R%28x%29-4=0%2B-+sqrt%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=4%2B-+sqrt%28x-1%29 ALIGN=MIDDLE  ALT=\"R%28x%29=4%2B-+sqrt%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The domain of R(x) is for TWO different functions.  R itself is a relation and not a function.  This is because the \"plus or minus\" part of the expression.  The domain for either branch of R  is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=4 ALIGN=MIDDLE  ALT=\"x%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Look again at function f(x).  Domain is ALL REAL NUMBERS.  What about the range of f(x)?   f(x) is a parabola with a vertex minimum value at  (4,1).  This means that the RANGE for f(x)  is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=4 ALIGN=MIDDLE  ALT=\"x%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or as a description, from 4 inclusive toward infinity.  \r<BR>\n" );
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document.write( "Going from a function  (f(x)) to its inverse, the domain and range switch.  The range <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=4 ALIGN=MIDDLE  ALT=\"x%3E=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for f(x)  is the DOMAIN for either branch of R(x).\r<BR>\n" );
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document.write( "Function f(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-3%2C12%2C-3%2C12%2C%28x-4%29%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-3%2C12%2C-3%2C12%2C%28x-4%29%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Upper branch of R(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-3%2C12%2C-7%2C8%2C-4%2Bsqrt%28x-1%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-3%2C12%2C-7%2C8%2C-4%2Bsqrt%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lower branch of R(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-3%2C12%2C-7%2C8%2C-4-sqrt%28x-1%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-3%2C12%2C-7%2C8%2C-4-sqrt%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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