document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196463>Question 1196463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a formula for the inverse of the function.<BR>\n" );
document.write( "f(x) = 6 − x2(x raised to the power of 2), x ≥ 0<BR>\n" );
document.write( "f −1(x) = \r<BR>\n" );
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document.write( "f(x) = 6 − x2, x ≥ 0<BR>\n" );
document.write( "f −1(x) = <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 #829303 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=829303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The standard template or outline to finding the inverse is this:<BR>\n" );
document.write( "1) Replace f(x) with y<BR>\n" );
document.write( "2) Swap x and y<BR>\n" );
document.write( "3) Solve for y to find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{f}^{-1}(\text{x})\">\r<BR>\n" );
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document.write( "So the steps look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+6+-+x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+6+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+6+-+x%5E2 ALIGN=MIDDLE  ALT=\"y+=+6+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply step 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6+-+y%5E2 ALIGN=MIDDLE  ALT=\"x+=+6+-+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply step 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%5E2+=+6 ALIGN=MIDDLE  ALT=\"x%2By%5E2+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+6-x ALIGN=MIDDLE  ALT=\"y%5E2+=+6-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%286-x%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%286-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The domain of f(x) 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;\" ><BR>\n" );
document.write( "The domain and range swap when going from the original function to the inverse (since the x and y swap roles)<BR>\n" );
document.write( "This means the range of the inverse 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;\" > and it further means we'll focus on the positive version of the square root only. We won't have \"plus/minus\".\r<BR>\n" );
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document.write( "Answer: The inverse is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{f}^{-1}(\text{x}) = \sqrt{6-\text{x}}\"><BR>\n" );
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