document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=483734>Question 483734</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=3x^2-x+10<BR>\n" );
document.write( "g(x)=1-20x\r<BR>\n" );
document.write( "\n" );
document.write( "Find find the inverse of both functions </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331072 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=331072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=3x^2-x+10<BR>\n" );
document.write( "g(x)=1-20x <BR>\n" );
document.write( "Find find the inverse of both functions<BR>\n" );
document.write( "**<BR>\n" );
document.write( "The procedure for finding the inverse of a function is to interchange x and y, then solve for y. In effect, you are solving x in terms of y.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "f(x)=3x^2-x+10<BR>\n" );
document.write( "y=3x^2-x+10<BR>\n" );
document.write( "interchange x and y<BR>\n" );
document.write( "x=3y^2-y+10<BR>\n" );
document.write( "3y^2-y+10=x<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "3(y^2-y/3+1/36)+10-1/12=x<BR>\n" );
document.write( "3(y-1/6)^2+120/12-1/12=x<BR>\n" );
document.write( "3(y-1/6)^2+119/12=x<BR>\n" );
document.write( "(y-1/6)^2=(x-119/12)/3<BR>\n" );
document.write( "(y-1/6)=±((x-119/12)/3)^.5<BR>\n" );
document.write( "y=±((x-119/12)/3)^.5+1/6 (This is the inverse of f(x))<BR>\n" );
document.write( "As seen by the graph below, f(x) and its inverse are parabolas<BR>\n" );
document.write( "..\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2C+%28%28x-119%2F12%29%2F3%29%5E.5%2B1%2F6%2C-%28%28x-119%2F12%29%2F3%29%5E.5%2B1%2F6%2C3x%5E2-x%2B10%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "g(x)=1-20x<BR>\n" );
document.write( "y=1-20x<BR>\n" );
document.write( "x=1-20y<BR>\n" );
document.write( "20y=1-x<BR>\n" );
document.write( "y=(1-x)/20 (This is the inverse of g(x))<BR>\n" );
document.write( "see the graph below:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2C1-20x%2C%281-x%29%2F20%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2C1-20x%2C%281-x%29%2F20%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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