document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085052>Question 1085052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is f (x+3) same with f(×) + f(3)<BR>\n" );
document.write( "show solution with explanation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699084 by </B><A HREF=/tutors/aboutme.mpl?userid=natolino_2017><B>natolino_2017(77)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=natolino_2017><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=699084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x+3) = f(x) + f(3), it means that f is a linear transformation.\r<BR>\n" );
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document.write( "so if f(x) = ax +b, \r<BR>\n" );
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document.write( "f(x+3) = a(x+3) + b = ax +3a +b\r<BR>\n" );
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document.write( "f(3) = 3a + b.\r<BR>\n" );
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document.write( "So if f(x+3) = f(x) + f(3)\r<BR>\n" );
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document.write( "      ax+3a+b = ax +b +3a +b\r<BR>\n" );
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document.write( "So b=0, and a any real number.\r<BR>\n" );
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document.write( "Answer: f(x) = ax with a any real number. \r<BR>\n" );
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document.write( "@natolino_ </SPAN>\n" );
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