document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=704329>Question 704329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a problem with fully understanding how to get an answer for these questions. I seriously do not understand how to get the domain, but I think I figured it out. If anyone can tell me where I went wrong it very simple terms that would be great. I apologize about there being more than 1 question. \r<BR>\n" );
document.write( "\n" );
document.write( "1. Find the indicated function value.f(x) = x - 2, g(x) = x + 1Find (f + g)(-1) <BR>\n" );
document.write( "Answer: -2 + 1 * -1 = 1<BR>\n" );
document.write( "2. Find the domain of the function.f(x) = -3x + 2<BR>\n" );
document.write( "Answer: (-&#8734;, &#8734;)<BR>\n" );
document.write( "3.For the pair of functions, determine the domain of f + g.f(x) = 2x + -9, g(x) = 4x + -3 <BR>\n" );
document.write( "Answer: (-&#8734;, 0) or (0, &#8734;)<BR>\n" );
document.write( "4. Find the requested value.f(x) = 2x2 - 1, g(x) = x + 1Find f(4) - g(4).<BR>\n" );
document.write( "Answer: 34 <BR>\n" );
document.write( "5. For the pair of functions, determine the domain of f + g.f(x) = 4x + 3, g(x) = 3x + 8<BR>\n" );
document.write( "Answer: (-&#8734;, -4) or (-4, &#8734;) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434033 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=434033\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. f(x) = x - 2, g(x) = x + 1<BR>\n" );
document.write( "What they mean by (f + g)(-1) is the function made by adding functions f and g applied to x=-1.<BR>\n" );
document.write( "You can calculate it as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29+%2B+g%28-1%29 ALIGN=MIDDLE  ALT=\"f%28-1%29+%2B+g%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= [(-1)-2] + [(-1)+1] =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3+%2B+0+=highlight%28-3%29 ALIGN=MIDDLE  ALT=\"-3+%2B+0+=highlight%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or you can calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%2Bg%29%28x%29=%28x-2%29%2B%28x%2B1%29=2x-1%2C+so+%7B%7B%7Bhighlight%28%7B%7B%7B%28f%2Bg%29%28x%29=2x-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then substitute (-1) for x to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%2Bg%29%28-1%29+=+2%28-1%29+-1+=+-2+-1+=+highlight%28-3%29 ALIGN=MIDDLE  ALT=\"%28f%2Bg%29%28-1%29+=+2%28-1%29+-1+=+-2+-1+=+highlight%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It is not a product, and it is not ( -2 + 1) * (-1 )= 1<BR>\n" );
document.write( " <BR>\n" );
document.write( "2. Find the domain of the function.f(x) = -3x + 2<BR>\n" );
document.write( "Answer: (-&#8734;, &#8734;)<BR>\n" );
document.write( "You are correct. The domain of a function is the set of x values where it is defined.<BR>\n" );
document.write( "Since there are no given restrictions on x,<BR>\n" );
document.write( "and you can calculate it for any x,<BR>\n" );
document.write( "the domain of f(x) = -3x + 2 is all real numbers.<BR>\n" );
document.write( "(That is true of all polynomials).<BR>\n" );
document.write( " <BR>\n" );
document.write( "3.For the pair of functions, determine the domain of f + g.f(x) = 2x + -9, g(x) = 4x + -3 <BR>\n" );
document.write( "Answer: (-&#8734;, 0) or (0, &#8734;)<BR>\n" );
document.write( "Why not (-&#8734;, &#8734;)?<BR>\n" );
document.write( "Do you think you could not calculate that function for x=0?<BR>\n" );
document.write( "Denominators should not be zero, but I do not see any denominator in that function.<BR>\n" );
document.write( " <BR>\n" );
document.write( "4.  If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E2-1 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=x%2B1 ALIGN=MIDDLE  ALT=\"g%28x%29=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%29=2%2A4%5E2-12%2A16-1=32-1=31 ALIGN=MIDDLE  ALT=\"f%284%29=2%2A4%5E2-12%2A16-1=32-1=31\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%284%29=4%2B1=5 ALIGN=MIDDLE  ALT=\"g%284%29=4%2B1=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%29-g%284%29=31-5=26 ALIGN=MIDDLE  ALT=\"f%284%29-g%284%29=31-5=26\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "5. f+g just indicates the function that is a sum of 2 functions.<BR>\n" );
document.write( "f(x) = 4x + 3, and g(x) = 3x + 8 are polynomial functions.<BR>\n" );
document.write( "They can be calculated for any real number x.<BR>\n" );
document.write( "The sum can always be calculated, for any x.<BR>\n" );
document.write( "The domain is all the real numbers<BR>\n" );
document.write( " <BR>\n" );
document.write( "UNDERSTANDING DOMAIN:<BR>\n" );
document.write( "The domain of a function is the set of x values where it is defined.<BR>\n" );
document.write( "Examples:<BR>\n" );
document.write( "If f(x) is defined as f(x) = 5 for all x>2,<BR>\n" );
document.write( "then its domain is (2, &#8734;) because it is not defined for x=2, or for any x<2.<BR>\n" );
document.write( "For a function without any explanation as to what x you are allowed to use,<BR>\n" );
document.write( "you have to figure out if there is any value of x that will not work.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not exist (cannot be calculated) for x<0,<BR>\n" );
document.write( "because there are no real square roots for negative numbers,<BR>\n" );
document.write( "so its domain is [0, &#8734;)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not exist for x=3, because that would make the denominator zero, and we cannot divide by zero.<BR>\n" );
document.write( "We cannot calculate the function for x=3, so 3 is not part of the domain.<BR>\n" );
document.write( "We can calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all other numbers so its domain is<BR>\n" );
document.write( "(-&#8734;, 3) or (3, &#8734;) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );