document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=612279>Question 612279</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(&#8730;(11)+&#8730;(15))<BR>\n" );
document.write( " f(x) = x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385602 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=385602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Function problems will be a lot easier for you once you learn that the \"x\" in f(x) is just a placeholder. It represents whatever happens to be the input to the function. And the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > part of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells use what the function does to its input, x. It squares it. No matter what the input is to this function f, it will square it. If the input is x, f will square it. If the input is 5, f will square it. If the input is q, f will square it. If the input is a-4, f will square it.<br><BR>\n" );
document.write( "If the input is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29+%2B+sqrt%2815%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29+%2B+sqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, as in f<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2811%29+%2B+sqrt%2815%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2811%29+%2B+sqrt%2815%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, f will square it! So:<BR>\n" );
document.write( "f<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2811%29+%2B+sqrt%2815%29%29+=+%28sqrt%2811%29%2Bsqrt%2815%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%2811%29+%2B+sqrt%2815%29%29+=+%28sqrt%2811%29%2Bsqrt%2815%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "All that is left is to simplify. Exponents <i>do not distribute!</i> So it is not just 11 + 15. To square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29%2Bsqrt%2815%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29%2Bsqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > correctly, use FOIL on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2811%29%2Bsqrt%2815%29%29%28sqrt%2811%29%2Bsqrt%2815%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2811%29%2Bsqrt%2815%29%29%28sqrt%2811%29%2Bsqrt%2815%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2+=+a%5E2+%2B2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2+=+a%5E2+%2B2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern. Personally, I prefer using the pattern:<BR>\n" );
document.write( "f<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2811%29+%2B+sqrt%2815%29%29+=+%28sqrt%2811%29%2Bsqrt%2815%29%29%5E2+=+%28sqrt%2811%29%29%5E2+%2B2%28sqrt%2811%29%29%28sqrt%2815%29%29+%2B+%28sqrt%2815%29%29%5E2+=+11+%2B+2sqrt%28165%29+%2B+15+=+26+%2B3sqrt%28165%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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