document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206027>Question 206027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for the one-to-one function f(x)= 2/x-4<BR>\n" );
document.write( "Find the inverse f^-1<BR>\n" );
document.write( "Find the domain and range of f<BR>\n" );
document.write( "Find the domain and range of f^-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156144 by </B><A HREF=/tutors/aboutme.mpl?userid=mickclns><B>mickclns(59)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mickclns><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=156144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%2Fx-4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%2Fx-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the inverse function of a function, replace x by y and y (or f(x) ) by x and solve for y<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2Fy-4 ALIGN=MIDDLE  ALT=\"x+=+2%2Fy-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >      add 4 to each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4+=+2%2Fy ALIGN=MIDDLE  ALT=\"x%2B4+=+2%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >     change the left side to a fraction and flip both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x%2B4%29+=+y%2F2 ALIGN=MIDDLE  ALT=\"1%2F%28x%2B4%29+=+y%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >     multiply both sides by 2, then switch sides so y (the inverse of f(x) ) is on the left<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29+=+y+=+2+%2F+%28x%2B4%29 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29+=+y+=+2+%2F+%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Here is a graph of f (red) and its inverse (green, the vertical line at -4 should be ignored, it is not part of either function). Also, graphed is the line y=x ... a function and its inverse are always mirror images of one another across this line, which you can see for the green and the red here.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C4%2C-10%2C4%2C%282%2Fx%29+-+4%2C+2%2F%28x%2B4%29%2C+x+%29+ ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C4%2C-10%2C4%2C%282%2Fx%29+-+4%2C+2%2F%28x%2B4%29%2C+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( "The domain of f is all real numbers except 0 (because x = x-0 is in the denominator makes f(x) undefined).<BR>\n" );
document.write( "The range of f is all real numbers except -4 ... for -4 to be the value of y, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fx ALIGN=MIDDLE  ALT=\"2%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > would have to be 0 which means x would have to be infinitely large, but no real number is infinitely large.<BR>\n" );
document.write( "The domain of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is all real numbers except -4 (because x+4 = -4+4 is in the denomiator and makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > undefined). <BR>\n" );
document.write( "The range of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is all real numbers except 0 ... for 0 to be the value of y, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"2%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > would have to be 0 which means x-4 (and therefore x) would have to be infinitely large, but no real number is infinitely large. </SPAN>\n" );
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