document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249140>Question 249140</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find f(g(2)) if f(x)=sqroot of x+2 and g(x)=2x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181510 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=181510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = sqrt(x+2)\r<BR>\n" );
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document.write( "g(x) = (2x+3)\r<BR>\n" );
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document.write( "you want:\r<BR>\n" );
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document.write( "f(g(2))\r<BR>\n" );
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document.write( "first find g(2)\r<BR>\n" );
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document.write( "in the equation of g(x) = (2x+3), you replace x with 2 to get:\r<BR>\n" );
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document.write( "g(2) = (2*2 + 3) = 4+3 = 7\r<BR>\n" );
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document.write( "in the equation of f(x) = sqrt(x+2), you replace x with g(x) to get:\r<BR>\n" );
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document.write( "f(g(x) = sqrt(g(x)+2)\r<BR>\n" );
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document.write( "since g(x) = 7, you replace g(x) with 7 to get:\r<BR>\n" );
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document.write( "f(7) = sqrt(7+2) = sqrt(9) = 3\r<BR>\n" );
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document.write( "the equation is the rules by which you relate the independent variable to the dependent variable.\r<BR>\n" );
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document.write( "the independent variable is the variable that does not depend on any rules to establish a value for it.\r<BR>\n" );
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document.write( "the dependent variable is the variable that depends on the rules of the equation to establish a value for it.\r<BR>\n" );
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document.write( "when x is a certain value, y has to be a certain value.\r<BR>\n" );
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document.write( "x is also called the argument of the function.\r<BR>\n" );
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document.write( "the argument of the function is the variable that the rules of the equation are working on.\r<BR>\n" );
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document.write( "y = f(x) = x^2 means the independent variable in the equation is x.\r<BR>\n" );
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document.write( "y = f(a) = a^2 means the independent variable in the equation is a.  \r<BR>\n" );
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document.write( "the rules are the same.\r<BR>\n" );
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document.write( "the only difference is the variable that the equation is working with.\r<BR>\n" );
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document.write( "that is why when you say f(x) = x^2, f(x) becomes the dependent variable and x is the independent variable.\r<BR>\n" );
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document.write( "when you say f(2) using the same equation, then the rules stay the same but the independent variable becomes 2 instead of x.\r<BR>\n" );
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document.write( "f(2) = 2^2 = 4.\r<BR>\n" );
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document.write( "when you say f(g(x)), then the independent variable in the equation becomes g(x).\r<BR>\n" );
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document.write( "g(x), however, was the dependent variable in another equation, so it's value had to be calculated before you could put it into f(g(x)).\r<BR>\n" );
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document.write( "that's exactly what we did above.\r<BR>\n" );
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document.write( "we solved for g(2) to get 7.\r<BR>\n" );
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document.write( "then we solved for f(g(x)) to get f(7) = 3.\r<BR>\n" );
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document.write( "you are placing g(x) into the argument of the equation f(x) = sqrt(x+2) which means you are replacing the existing argument of x with the argument of g(x).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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