document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116015>Question 116015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain of the following:\r<BR>\n" );
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document.write( "g(t)=5^t </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84386 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=84386\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d)\r<BR>\n" );
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document.write( "If you have something like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you have to keep in mind that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > since division by zero is undefined. If you have something like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you have to keep in mind that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > since you cannot take the square root of a negative number. If you have something like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%29 ALIGN=MIDDLE  ALT=\"log%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29 ALIGN=MIDDLE  ALT=\"ln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you have to keep in mind that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E0 ALIGN=MIDDLE  ALT=\"x%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > since you cannot take the log of zero or a negative number. These are examples of restrictions of the domain.\r<BR>\n" );
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document.write( "Since the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28t%29=5%5Et ALIGN=MIDDLE  ALT=\"g%28t%29=5%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not have a division by x, a square root, or a logarithm function, this means we don't have to worry about domain restrictions. \r<BR>\n" );
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document.write( "Also, notice if we graph the function, we can see that there are no domain restrictions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+5%5Ex%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+5%5Ex%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28t%29=5%5Et ALIGN=MIDDLE  ALT=\"g%28t%29=5%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the domain is the set of all real numbers. In other words, t can be any real number.\r<BR>\n" );
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document.write( "Here's the domain in interval notation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,\infty\right)\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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