document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72596>Question 72596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me solve\r<BR>\n" );
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document.write( "g(h(15))\r<BR>\n" );
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document.write( "if<BR>\n" );
document.write( "g(x)=70<BR>\n" );
document.write( "h(x)= -x^2 + 6x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51899 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=70 ALIGN=MIDDLE  ALT=\"g%28x%29=70\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=+-x%5E2+%2B+6x ALIGN=MIDDLE  ALT=\"h%28x%29=+-x%5E2+%2B+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You are then asked to find g(h(15))<BR>\n" );
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document.write( "Once you understand the process, you can do this one by inspection.  But let's work it<BR>\n" );
document.write( "the \"long\" way.  What this problem tells you to do is to first find h(15).  To do that means<BR>\n" );
document.write( "to just take the equation for h(x) and substitute 15 for all the x's in the equation.<BR>\n" );
document.write( "Doing that results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2815%29+=+-%2815%5E2%29+%2B+6%2A15+=+-225+%2B+90+=+-135 ALIGN=MIDDLE  ALT=\"h%2815%29+=+-%2815%5E2%29+%2B+6%2A15+=+-225+%2B+90+=+-135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you know that h(15) = -135 and since you are being asked to find g(h(15)) you can<BR>\n" );
document.write( "substitute -135 for h(15).  Therefore, you are being asked to find g(-135) which tells you<BR>\n" );
document.write( "to go to the equation for g(x) and substitute -135 every where that x appears in the equation.<BR>\n" );
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document.write( "Note now that there are no x terms in the right side of the equation for g(x).  So you can<BR>\n" );
document.write( "write that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28-135%29+=+70 ALIGN=MIDDLE  ALT=\"g%28-135%29+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "because there is nothing on the right side where a substitution can be made.  Therefore,<BR>\n" );
document.write( "the answer to your problem is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28h%28x%29%29+=+g%28-135%29+=+70 ALIGN=MIDDLE  ALT=\"g%28h%28x%29%29+=+g%28-135%29+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "With a little more practice and experience you could have looked at the expression for<BR>\n" );
document.write( "g(x) and recognized that no matter what x was (a number or in this case h(x)) it wouldn't<BR>\n" );
document.write( "change the right side of g(x).  g(x) would always be 70.<BR>\n" );
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document.write( "Hope this adds a little to your understanding of terms such as g(x), b(x), m(x), and so forth.<BR>\n" );
document.write( "  </SPAN>\n" );
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