document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148429>Question 1148429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether f and g are inverse functions by evaluating f(g(x)) and g(f(x)).\r<BR>\n" );
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document.write( "f(x)=x^2-2, domain [0, ∞)<BR>\n" );
document.write( "g(x)= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+x%2B+2+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+x%2B+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , domain [-2,∞)\r<BR>\n" );
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document.write( "Evaluate f(g(x)).<BR>\n" );
document.write( "f(g(x))= (Simplify your answer.)\r<BR>\n" );
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document.write( "Evaluate g(f(x)).<BR>\n" );
document.write( "g(f(x))= (Simplify your answer.)\r<BR>\n" );
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document.write( "Are f(x) and g(x) inverse functions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #769799 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=769799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> these look like inverses of each other because f(g(x)) = x and g(f(x)) = x.\r<BR>\n" );
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document.write( "here's a reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://home.windstream.net/okrebs/page45.html\" target = \"_blank\">http://home.windstream.net/okrebs/page45.html</a>\r<BR>\n" );
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document.write( "you have f(x) = x^2-2.<BR>\n" );
document.write( "the domain is [0,infinity)<BR>\n" );
document.write( "the range is [-2,infinity)\r<BR>\n" );
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document.write( "you have g(x) = sqrt(x+2)<BR>\n" );
document.write( "the domain is [-2,infinity)<BR>\n" );
document.write( "the range is [0,infinity)\r<BR>\n" );
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document.write( "here's the graph of f(x) = x^2-2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/110801.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "here's the graph of g(x) = sqrt(x+2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/110802.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "you solve for f(g(x)) as follows:\r<BR>\n" );
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document.write( "f(x) = x^2-2<BR>\n" );
document.write( "g(x) = sqrt(x+2)<BR>\n" );
document.write( "to get f(g(x)), you replace the x in f(x) with g(x).<BR>\n" );
document.write( "this means you relace the x in f(x) with sqrt(x+2).<BR>\n" );
document.write( "f(g(x)) = (sqrt(x+2))^2-2 = x+2-2 = x\r<BR>\n" );
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document.write( "g(x) = sqrt(x+2)<BR>\n" );
document.write( "f(x) = x^2-2<BR>\n" );
document.write( "to get g(f(x)), you replace the x in g(x) with f(x).<BR>\n" );
document.write( "this means you replace the x in g(x) with x^2-2.<BR>\n" );
document.write( "g(f(x)) = sqrt(x^2-2+2) = sqrt(x^2) = x\r<BR>\n" );
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document.write( "since f(g(x)) = x and g(f(x)) = x, then the two functions are inverse functions to each other.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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