document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169816>Question 169816</A>: <I><SPAN STYLE=\"word-break: break-all;\">      <BR>\n" );
document.write( "Determine if given function is one to one.  If it is, find the formula for the inverse.\r<BR>\n" );
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document.write( "f(x)=5x-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125216 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=125216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> since for every value of x, you get one unique f(x), the equation is a function.<BR>\n" );
document.write( "to solve for the inverse do the following:<BR>\n" );
document.write( "let y = f(x)<BR>\n" );
document.write( "then y = 5x - 6<BR>\n" );
document.write( "substitute x for y and y for x.<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "x = 5y - 6<BR>\n" );
document.write( "solve for y:<BR>\n" );
document.write( "add 6 to both sides of equation:<BR>\n" );
document.write( "x + 6 = 5y<BR>\n" );
document.write( "divide both sides of equation by 5:<BR>\n" );
document.write( "(x+6)/5 = y<BR>\n" );
document.write( "let y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x)<BR>\n" );
document.write( "you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x) = (x+6)/5 which is the inverse function of f(x) = 5x-6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to prove this is an inverse equation, solve for a known value of x in f(x).<BR>\n" );
document.write( "f(5) = 5*5-6 = 25-6 = 19<BR>\n" );
document.write( "the solution set for f(5) is (5,19)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "take the inverse function of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x) = (x+6)/5<BR>\n" );
document.write( "and solve for x = 19 (this is f(x)).<BR>\n" );
document.write( "your inverse function starts off as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >(x) = (x+6)/5<BR>\n" );
document.write( "you substitute f(x) for x.<BR>\n" );
document.write( "since f(x) = 19 which you just solved for when x = 5, then your inverse equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >(19) = (19+6)/5<BR>\n" );
document.write( "the right side of this equation becomes:<BR>\n" );
document.write( "(19+6)/5 = 25/5 = 5<BR>\n" );
document.write( "your solution set for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >(19) is (19,5)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "f(x) solution set is (5,19)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >(f(x)) solution set is (19,5)<BR>\n" );
document.write( "since the x value in the original equation equals the y value in the inverse function equation, this is good.<BR>\n" );
document.write( "since the y value in the original equation equals the x value in the inverse function equation, this is also good.<BR>\n" );
document.write( "it means that the inverse function was calculated correctly.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "note:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1 ALIGN=MIDDLE  ALT=\"f%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > means the inverse function of f(x)<BR>\n" );
document.write( "it does not mean f to the -1 power.<BR>\n" );
document.write( "i didn't know how to show it so i used the exponent notation.<BR>\n" );
document.write( "-----\r<BR>\n" );
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document.write( " </SPAN>\n" );
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