document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73816>Question 73816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the questions are from a hand out\r<BR>\n" );
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document.write( " 1. Find the inverse of   f(x)=3x+1 where f:R arrow R\r<BR>\n" );
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document.write( " 2. If f(x) = x-3 g(x)=2x+5 find fog and gof \r<BR>\n" );
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document.write( " 3. If f(x) = x^2 + 3x-5 then f(-2)=\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 #52868 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52868\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First Problem:   Find the inverse of   f(x)=3x+1<BR>\n" );
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document.write( "I'm not exactly sure what you mean by \"f:R arrow R\". I suspect it has something to do with<BR>\n" );
document.write( "mapping.  But as to finding the inverse of f(x) ... this is a 4 step process.<BR>\n" );
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document.write( "Step 1. Replace f(x) with \"y\" so that your equation becomes:<BR>\n" );
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document.write( "y = 3x + 1<BR>\n" );
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document.write( "Step 2. Change the y to x and the x to y so that the equation is then:<BR>\n" );
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document.write( "x = 3y + 1<BR>\n" );
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document.write( "Step 3. Solve the equation that you got in Step 2 for y.<BR>\n" );
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document.write( "Remove the 3y term from the right side by subtracting 3y from both sides. After this subtraction<BR>\n" );
document.write( "the equation is then:<BR>\n" );
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document.write( "-3y + x = 1<BR>\n" );
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document.write( "Remove the x term from the left side by subtracting x from both sides to get:<BR>\n" );
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document.write( "-3y = -x + 1<BR>\n" );
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document.write( "Divide both sides (all terms) by -3 and you then have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%2F3%29+%2B+%28-1%2F3%29 ALIGN=MIDDLE  ALT=\"y+=+%28x%2F3%29+%2B+%28-1%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Step 4. Replace y with the inverse notation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29=+x%2F3+-+1%2F3 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29=+x%2F3+-+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the inverse of the function you were given.<BR>\n" );
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document.write( "Second problem: If f(x) = x-3 and g(x)=2x+5 find fog and gof<BR>\n" );
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document.write( "fog is found by replacing every x that appears in f(x) with the right side of g(x) and then<BR>\n" );
document.write( "simplifying the result.<BR>\n" );
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document.write( "First the replacement of the x's on the right side of f(x):<BR>\n" );
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document.write( "fog = (2x+5) - 3<BR>\n" );
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document.write( "then simplify by removing the parentheses and adding +5 and -3 to get:<BR>\n" );
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document.write( "fog = 2x + 2<BR>\n" );
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document.write( "That's what you are looking for.<BR>\n" );
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document.write( "Next find gof.  This involves the same process as before. In gof you replace each of the<BR>\n" );
document.write( "x's on the right side with the right side of f(x) to get:<BR>\n" );
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document.write( "gof = 2(x-3) + 5<BR>\n" );
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document.write( "Now simplify starting with doing the multiplication to get:<BR>\n" );
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document.write( "gof = 2x - 6 + 5<BR>\n" );
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document.write( "then combine the -6 and +5 to get:<BR>\n" );
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document.write( "gof = 2x - 1<BR>\n" );
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document.write( "And that's the answer.<BR>\n" );
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document.write( "Final problem. If f(x) = x^2 + 3x - 5 then f(-2)=<BR>\n" );
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document.write( "In f(x) replace every x with -2 and then simplify:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29+=+%28-2%29%5E2+%2B+3%28-2%29+-+5 ALIGN=MIDDLE  ALT=\"f%28-2%29+=+%28-2%29%5E2+%2B+3%28-2%29+-+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then simplify:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29+=+4+-+6+-+5 ALIGN=MIDDLE  ALT=\"f%28-2%29+=+4+-+6+-+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "combine to get the answer of f(-2) = -7<BR>\n" );
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document.write( "There you go.<BR>\n" );
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document.write( "Hope this helps you to understand the basic ideas behind all these operations.  </SPAN>\n" );
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