document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209612>Question 1209612</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the domain of f is (-1,1). Define the function g by<BR>\n" );
document.write( "g(x) = 5 - f(x) + f(5/x).<BR>\n" );
document.write( "What is the domain of g?<BR>\n" );
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document.write( "f(5/x) is what we should focus on.<BR>\n" );
document.write( "The input 5/x needs to be on the interval -1 < 5/x < 1, so it fits with the domain interval (-1,1).\r<BR>\n" );
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document.write( "You should find that -1 < 5/x < 1 leads to either x < -5 or x > 5.<BR>\n" );
document.write( "But none of those values are in the interval -1 < x < 1.\r<BR>\n" );
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document.write( "Therefore the <font color=red>domain of g(x) is the empty set</font>.\r<BR>\n" );
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document.write( "Some examples:\r<BR>\n" );
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document.write( "Let's try x = 0.5<BR>\n" );
document.write( "g(x) = 5 - f(x) + f(5/x)<BR>\n" );
document.write( "g(0.5) = 5 - f(0.5) + f(5/0.5)<BR>\n" );
document.write( "g(0.5) = 5 - f(0.5) + <font color=red>f(10)</font><BR>\n" );
document.write( "g(0.5) = 5 - f(0.5) + <font color=red>undefined</font><BR>\n" );
document.write( "g(0.5) = <font color=red>undefined</font><BR>\n" );
document.write( "This shows that x = 0.5 is not in the domain of g(x).<BR>\n" );
document.write( "f(10) is undefined since f(x) is only defined when -1 < x < 1.\r<BR>\n" );
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document.write( "Let's try x = 10<BR>\n" );
document.write( "g(x) = 5 - f(x) + f(5/x)<BR>\n" );
document.write( "g(10) = 5 - f(10) + f(5/10)<BR>\n" );
document.write( "g(10) = 5 - <font color=red>f(10)</font> + f(0.5)<BR>\n" );
document.write( "g(10) = 5 - <font color=red>undefined</font> + f(0.5)<BR>\n" );
document.write( "g(10) = <font color=red>undefined</font><BR>\n" );
document.write( "We run into the same problem as before.<BR>\n" );
document.write( "This shows that x = 10 is not in the domain of g(x).\r<BR>\n" );
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document.write( "I encourage the student to explore other examples.<BR>\n" );
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