document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=69704>Question 69704</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131870270/algebrahomeworkh>College Algebra-An Early Functions Approach</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> This question is from a study handout, not the book per se. This is finding the inverse of a one to one function. The question is:\r<BR>\n" );
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document.write( "f(x)=7/3x-2\r<BR>\n" );
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document.write( "I start by substituting y for f(x)=y=7/3x-2\r<BR>\n" );
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document.write( "Then I switch y for x= x=7/3y-2\r<BR>\n" );
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document.write( "Next I multiple both sides of the equation by 3y-2 to elimate the fraction=<BR>\n" );
document.write( "x(3y-2)=7(3y-2)<BR>\n" );
document.write( "=3xy-2x=21y-14\r<BR>\n" );
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document.write( "Then I isolate the y variables= 3xy-21y=2x-14\r<BR>\n" );
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document.write( "Next I remove the common factor of 3y= 3y(x-7)=2x-14\r<BR>\n" );
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document.write( "I'm assuming the next step would be to divide both sides by x-7. That would give me: 3y=2x-14/x-7\r<BR>\n" );
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document.write( "It seems to me that would give me 3y=2, and the final answer would be y=2/3.\r<BR>\n" );
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document.write( "My answer key says the correct answer is f(inverse x)=7/3x+2/3.\r<BR>\n" );
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document.write( "No matter how many times I try this, I can't figure out where they're getting the 7/3x from. \r<BR>\n" );
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document.write( "Thank you so much for your help!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49657 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=49657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the inverse of:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+7%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+7%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+7%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"y+=+7%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Swap the x and y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F%283y-2%29 ALIGN=MIDDLE  ALT=\"x+=+7%2F%283y-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for y. Multiply both sides by (3y-2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%283y-2%29+=+7 ALIGN=MIDDLE  ALT=\"x%283y-2%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283y-2%29+=+7%2Fx ALIGN=MIDDLE  ALT=\"%283y-2%29+=+7%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+7%2Fx+%2B+2 ALIGN=MIDDLE  ALT=\"3y+=+7%2Fx+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+7%2F3x+%2B+2%2F3 ALIGN=MIDDLE  ALT=\"y+=+7%2F3x+%2B+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite as the inverse of the function.:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29+=+7%2F3x+%2B+2%2F3 ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29+=+7%2F3x+%2B+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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