document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112746>Question 112746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x)=square root of x-1 find f-1(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82192 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think you mean: If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=sqrt%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=sqrt%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The first thing you have to do is determine whether <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > exists.  There is a pretty simple test that will tell you.  It is called the horizontal line test.\r<BR>\n" );
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document.write( "Step 1: Graph the original function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C5%2C-2%2C5%2Csqrt%28x-1%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C5%2C-2%2C5%2Csqrt%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2:  If ANY possible horizontal line intersects the graph in more than one place, then we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a function, i.e. f does NOT have an inverse.  Otherwise, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > does exist and f does have an inverse.  For this example, there is no horizontal line that intersects the graph more than once, so we know that f has an inverse.  Now, and only now, can we set about finding it.\r<BR>\n" );
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document.write( "Procedure to find the inverse of a one-to-one function (one that has an inverse):\r<BR>\n" );
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document.write( "Step 1:  Replace f(x) with y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28x-1%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2:  Swap the positions of the x and y variables with each other.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28y-1%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28y-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3:  Rearrange the equation so that it again is showing y as a function of x, i.e. solve for y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28y-1%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28y-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=x%5E2=y-1 ALIGN=MIDDLE  ALT=\"x%5E2=y-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B1 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Ok, Super-Double-Plus Extra Credit.  If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > exist?\r<BR>\n" );
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document.write( "Hope this helps<BR>\n" );
document.write( "John </SPAN>\n" );
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