document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157561>Question 1157561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose f(x) = √x − 1 and g(x) = x^2 + 5. Find and simplify expressions for each of the following:\r<BR>\n" );
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document.write( "(a) (f ◦ g)(x)\r<BR>\n" );
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document.write( "(b) (g ◦ f)(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780454 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Suppose \r<BR>\n" );
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document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+x%5E2+%2B+5 ALIGN=MIDDLE  ALT=\"g%28x%29+=+x%5E2+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Find :<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+ ALIGN=MIDDLE  ALT=\"f+\"   DISABLED_style= \"max-width:90%; height:auto;\" >◦ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29\"   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=f+ ALIGN=MIDDLE  ALT=\"f+\"   DISABLED_style= \"max-width:90%; height:auto;\" >◦ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28+x%5E2+%2B+5%29 ALIGN=MIDDLE  ALT=\"f%28+x%5E2+%2B+5%29\"   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=f+ ALIGN=MIDDLE  ALT=\"f+\"   DISABLED_style= \"max-width:90%; height:auto;\" >◦ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%5E2+%2B+5%29-+1+%29+ ALIGN=MIDDLE  ALT=\"sqrt%28%28x%5E2+%2B+5%29-+1+%29+\"   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=f+ ALIGN=MIDDLE  ALT=\"f+\"   DISABLED_style= \"max-width:90%; height:auto;\" >◦ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2+%2B4+%29+ ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2+%2B4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b)\r<BR>\n" );
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document.write( " (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > ◦ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<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;\" >\r<BR>\n" );
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document.write( " (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > ◦ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28sqrt%28x+-+1%29%29 ALIGN=MIDDLE  ALT=\"g%28sqrt%28x+-+1%29%29\"   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=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > ◦ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x+-+1%29%29%5E2%2B5 ALIGN=MIDDLE  ALT=\"%28sqrt%28x+-+1%29%29%5E2%2B5\"   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=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > ◦ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+1%2B5 ALIGN=MIDDLE  ALT=\"x+-+1%2B5\"   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=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > ◦ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29 ALIGN=MIDDLE  ALT=\"%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );