document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394131>Question 394131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the function f(x)=x^2+x and g(x)=x-5<BR>\n" );
document.write( "a. Find h(x)=(f&#9702;g)(x).<BR>\n" );
document.write( "b. State the domain of h(x)=f&#9702;g)(x).<BR>\n" );
document.write( "c. Find h(x)=(g&#9702;f)(x).<BR>\n" );
document.write( "d. State the domain of h(x)=(g&#9702;f)(x). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279678 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=279678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using the function f(x)=x^2+x and g(x)=x-5<BR>\n" );
document.write( "a. Find h(x)=(f&#9702;g)(x).<BR>\n" );
document.write( "fog(x) = f[x-5]= (x-5)^2+(x-5) = x^2-10x+25+x-5 = x^2-9x+20<BR>\n" );
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document.write( "b. State the domain of h(x)=f&#9702;g)(x).<BR>\n" );
document.write( "The domain of g is All Real Numbers<BR>\n" );
document.write( "The range that g produces is All Real Numbers<BR>\n" );
document.write( "So the domain of f is All Real Numbers<BR>\n" );
document.write( "Conclusion: The domain of fog(x) is All Real Numbers<BR>\n" );
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document.write( "c. Find h(x)=(g&#9702;f)(x)= g[x^2+x] = x^2+x-5<BR>\n" );
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document.write( "d. State the domain of h(x)=(g&#9702;f)(x).<BR>\n" );
document.write( "The domain of f is R<BR>\n" );
document.write( "The Range of f is >=-1/4<BR>\n" );
document.write( "So the domain of g is >=-1/4<BR>\n" );
document.write( "Conclusion: The domain of gof(x) is x>=-1/4<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );