document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114569>Question 114569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been working on this problem for about an hour. I am ready to toss it out the window! <BR>\n" );
document.write( "1) Let f(x) compute the time in hours to travel x miles at 58 miles per hour. <BR>\n" );
document.write( "2)What does f-1(x) compute? \r<BR>\n" );
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document.write( "Thanks so much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83345 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=83345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1\r<BR>\n" );
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document.write( "If we use the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=rt ALIGN=MIDDLE  ALT=\"D=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then solving for t we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=D%2Fr ALIGN=MIDDLE  ALT=\"t=D%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since we know that we're traveling at 58 mph, this means r=58. So we then get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=D%2F58 ALIGN=MIDDLE  ALT=\"t=D%2F58\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now since we want to find the time based on a given distance, t will be dependent on D (whatever D is, t will be affected by it). So this means D is x (our input) and t is f(x) (our output)\r<BR>\n" );
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document.write( "So our equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%2F58 ALIGN=MIDDLE  ALT=\"f%28x%29=x%2F58\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So if we traveled 58 miles, then we simply plug it in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=58%2F58 ALIGN=MIDDLE  ALT=\"f%28x%29=58%2F58\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1 ALIGN=MIDDLE  ALT=\"f%28x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since f(x) is t, the time it takes to travel 58 miles going 58 mph is 1 hour.\r<BR>\n" );
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document.write( "#2\r<BR>\n" );
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document.write( "Now to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, simply switch x and f(x) to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=f%28x%29%2F58 ALIGN=MIDDLE  ALT=\"x=f%28x%29%2F58\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now solve for f(x)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58x=f%28x%29 ALIGN=MIDDLE  ALT=\"58x=f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 58\r<BR>\n" );
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document.write( "So our inverse function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29=58x ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29=58x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now heres what happened: When I switched x and f(x), I really switched t and D. So now the distance D is dependent on the time t (whatever t is, D will be derived from t). So for the inverse, x is now t and f(x) is now D. Basically, the inverse now computes the distance given a certain time (instead of a certain computing a certain time given a distance). \r<BR>\n" );
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document.write( "Is this making sense? </SPAN>\n" );
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