document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182951>Question 1182951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that function f : x maps to 2/ax + b , such that f(0) = -2 and f(2) = 2, Find the values of a and of b, find the values of x for which f(x) = x , Show that f(p) + f(-p) = 2f(p^2)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813062 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Will assume that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%2F%28ax%2Bb%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%2F%28ax%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f(0) = -2 ==> f(0) = 2/b = -2  ==>  b = -1  ==>   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%2F%28ax-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%2F%28ax-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f(2) = 2  ==>  2/(2a - 1) = 2  ==> a = 1  ==>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f(x) = x ==>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x-1%29+=+x ALIGN=MIDDLE  ALT=\"2%2F%28x-1%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ==> 2 = x(x-1)  ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-2=0 ALIGN=MIDDLE  ALT=\"x%5E2-x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<==> (x-2)(x+1) = 0  ==> x = 2 or -1.\r<BR>\n" );
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document.write( "Finally, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28p%29+%2B+f%28-p%29+=++2%2F%28p-1%29+%2B+2%2F%28-p-1%29+=+2%2A%28%28-2%29%2F%281-p%5E2%29%29+=+2%2A%282%2F%28p%5E2-1%29%29+=+2f%28p%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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