document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194818>Question 1194818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the functions 𝑓(𝑥) = √25 − 𝑥 , 𝑔(𝑥) = 𝑥^2+ 9 , ℎ(𝑥) = √𝑥 − 5<BR>\n" );
document.write( "a) Obtain the domains of each given function.<BR>\n" );
document.write( "b) Calculate the domain and rule of ℎ ∘ 𝑔 .<BR>\n" );
document.write( "c) Calculate the domain of 𝑔 ∘ 𝑓 . </SPAN>\n" );
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document.write( "Given the functions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+sqrt%2825+-+x%29++ ALIGN=MIDDLE  ALT=\"f%28x%29+=+sqrt%2825+-+x%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+x%5E2%2B+9+ ALIGN=MIDDLE  ALT=\"g%28x%29+=+x%5E2%2B+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29+=+sqrt%28x+-5%29 ALIGN=MIDDLE  ALT=\"h%28x%29+=+sqrt%28x+-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a) Obtain the domains of each given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+sqrt%2825+-+x%29++ ALIGN=MIDDLE  ALT=\"f%28x%29+=+sqrt%2825+-+x%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since given  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825+-+x%29 ALIGN=MIDDLE  ALT=\"sqrt%2825+-+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+-+x ALIGN=MIDDLE  ALT=\"25+-+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >must be zero or greater than zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+-+x%3E=0 ALIGN=MIDDLE  ALT=\"25+-+x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+%3E=x ALIGN=MIDDLE  ALT=\"25+%3E=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "domain: { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=25 ALIGN=MIDDLE  ALT=\"x%3C=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+x%5E2%2B+9+ ALIGN=MIDDLE  ALT=\"g%28x%29+=+x%5E2%2B+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "domain: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > (all real numbers)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29+=+sqrt%28x+-5%29 ALIGN=MIDDLE  ALT=\"h%28x%29+=+sqrt%28x+-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since given  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x+-+5%29 ALIGN=MIDDLE  ALT=\"sqrt%28x+-+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+5%3E=0 ALIGN=MIDDLE  ALT=\"x+-+5%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=5 ALIGN=MIDDLE  ALT=\"x+%3E=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "domain: { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=5 ALIGN=MIDDLE  ALT=\"x+%3E=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "b) Calculate the domain and rule of ℎ ∘ 𝑔 .\r<BR>\n" );
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document.write( "ℎ ∘𝑔 =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28g%28x%29%29=h%28x%5E2%2B+9%29=+sqrt%28x%5E2%2B+9+-5%29=sqrt%28x%5E2%2B+4%29 ALIGN=MIDDLE  ALT=\"h%28g%28x%29%29=h%28x%5E2%2B+9%29=+sqrt%28x%5E2%2B+9+-5%29=sqrt%28x%5E2%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <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;\" > is always positive no matter what <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > value is,\r<BR>\n" );
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document.write( "domain: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > (all real numbers)\r<BR>\n" );
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document.write( "c) Calculate the domain of 𝑔 ∘ 𝑓 .\r<BR>\n" );
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document.write( "𝑔 ∘𝑓 =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29=g%28sqrt%2825+-+x%29+%29=%28sqrt%2825+-+x%29+%29%5E2%2B+9=25-x%2B9=34-x ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=g%28sqrt%2825+-+x%29+%29=%28sqrt%2825+-+x%29+%29%5E2%2B+9=25-x%2B9=34-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "domain: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > (all real numbers)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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