document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035254>Question 1035254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A2. Suppose the point (1, 2) lies on the graph of the function f.<BR>\n" );
document.write( "(a) Find a point on the graph of the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29 ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28y%29=y-1%2Barctan+%28y%2F2%29 ALIGN=MIDDLE  ALT=\"g%28y%29=y-1%2Barctan+%28y%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "(b) Find two points on the graph of the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28h%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28h%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where h(x) = x^2 &#8722;&#960;x+ (cos^2)x.\r<BR>\n" );
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document.write( "Thankyou for looking over. Please provide some steps to steps instructions if possible. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649918 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=649918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose the point (1, 2) lies on the graph of the function f.<BR>\n" );
document.write( "(a) Find a point on the graph of the function g(f(x)), where g(y)=y-1+arctan (y/2).<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "g[f(1)] = g(2) = 2-1+arctan(2/2) = 2-1+pi/4 = 1+pi/4<BR>\n" );
document.write( "Point:: (1,g(f(1)) = (1,1+pi/4)<BR>\n" );
document.write( "-----------------------------------\r<BR>\n" );
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document.write( "(b) Find two points on the graph of the function f(h(x)), <BR>\n" );
document.write( "where  h(x) = x^2 &#8722;&#960;x+ (cos^2)x<BR>\n" );
document.write( "f[h(x)] = f[x^2-pi*x+cos^2(x)]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Remember f(1) = 2, so::<BR>\n" );
document.write( "If  x^2-pi*x+cos^2(x) = 1<BR>\n" );
document.write( "then x^2-pi = 1-cos^2(x) <BR>\n" );
document.write( "and x^2-pi*x = sin^2(x)<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "So f[x^2-pi*x+cos^2(x)] = f[sin^2+cos^2] = f(1) = 2<BR>\n" );
document.write( "Point:: (x,f[h(x)]) = (1,2)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "If x = pi<BR>\n" );
document.write( "then x^2-pi*x+cos^2(x) = pi^2 - pi^2 + 1 = 1<BR>\n" );
document.write( "Point:: (x,f[h(x)]  (pi,2)<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "Thankyou for looking over. Please provide some steps to steps instructions if possible. </SPAN>\n" );
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