document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=681109>Question 681109</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve whether or not the functions are inverses of each other?\r<BR>\n" );
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document.write( "1)F(x)=6x-7, g(x)=(x-6)/7\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "2) f(x)=3/(x+7), g(x)=(7x+3)/x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #422570 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=422570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tell whether or not the functions are inverses of each other?\r<BR>\n" );
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document.write( "1)F(x)=6x-7, g(x)=(x-6)/7\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "2) f(x)=3/(x+7), g(x)=(7x+3)/x\r<BR>\n" );
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document.write( "<br> If they are inverses, then their composite functions have to equal x <br><BR>\n" );
document.write( "That is f(g(x))=x and g(f(x))=x.\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=f%28%28x-6%29%2F7%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=f%28%28x-6%29%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You will substitute g(x) in for the x's in f(x).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=6%28%28x-6%29%2F7%29-7 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=6%28%28x-6%29%2F7%29-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%286x-36%29%2F7-7 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%286x-36%29%2F7-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Get a common denominator...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%286x-36%29%2F7-49%2F7 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%286x-36%29%2F7-49%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=%286x-85%29%2F7 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=%286x-85%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since it did not simplify to x, they are not inverses of each other.\r<BR>\n" );
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document.write( "<br>2. f(g(x))=f((7x+3)/x)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3%2F%28%287x%2B3%29%2Fx%2B7%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3%2F%28%287x%2B3%29%2Fx%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply the top and the bottom by x to clear the complex fraction.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3x%2F%28x%287x%2B3%29%2Fx%2B7x%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3x%2F%28x%287x%2B3%29%2Fx%2B7x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3x%2F%287x%2B3%2B7x%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3x%2F%287x%2B3%2B7x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3x%2F%2814x%2B3%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3x%2F%2814x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This also doesn't simplify to x and therefore are not inverses.\r<BR>\n" );
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document.write( "Just to clarify....this is an example where they ARE inverses.<BR>\n" );
document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=3%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%283%2Bx%29%2Fx ALIGN=MIDDLE  ALT=\"g%28x%29=%283%2Bx%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=f%28%283%2Bx%29%2Fx%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=f%28%283%2Bx%29%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3%2F%28%28%283%2Bx%29%2Fx%29-1%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3%2F%28%28%283%2Bx%29%2Fx%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to clear the complex fraction, multiply the top and bottom by x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3x%2F%28x%283%2Bx%29%2Fx-x%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3x%2F%28x%283%2Bx%29%2Fx-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3x%2F%283%2Bx-x%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3x%2F%283%2Bx-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=3x%2F3 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=3x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=x ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f(x) and g(x) ARE inverses in this case because f(g(x))=x.  <BR>\n" );
document.write( "*Note...g(f(x))=x as well....give it a try.\r<BR>\n" );
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document.write( "Hope that helped.  Happy Calculating!!!! </SPAN>\n" );
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