document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074102>Question 1074102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I need to find g(x), the inverse function of f(x)=log_2(4x)-2. I would also like an explanation on how to approach the problem so I can try to figure out how you're supposed to solve this. Any help would be very much appreciated. Thanks!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688856 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=688856\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let y = f(x).\r<BR>\n" );
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document.write( "you get y = log2(4x) - 2\r<BR>\n" );
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document.write( "replace y with x and x with y to get x = log2(4y) - 2\r<BR>\n" );
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document.write( "add 2 to both sides of the equation to get x + 2 = log2(4y)\r<BR>\n" );
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document.write( "by the basic definition of logarithms, x + 2 = log2(4y) if and only if 2^(x+2) = 4y\r<BR>\n" );
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document.write( "divide both sides of this equation by 4 to get (2^(x+2))/4 = y\r<BR>\n" );
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document.write( "that's the same as y = (2^(x+2)/4.\r<BR>\n" );
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document.write( "that's your inverse equation.\r<BR>\n" );
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document.write( "you know it's an inverse eqution if (x,y) from the original equaiton is equal to (y,x) from the inverse equation.\r<BR>\n" );
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document.write( "let x = 5,\r<BR>\n" );
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document.write( "f(x) = log2(4*5) - 2 which becomes f(x) = log2(20)-2\r<BR>\n" );
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document.write( "since log2(20) = log(20)/log(2), this equation becomes f(x) = log(20)/log(2) - 2\r<BR>\n" );
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document.write( "use the log function of your calculator to get log(20)/log(2) - 2 = 2.321928095\r<BR>\n" );
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document.write( "(x,y) from the original equation is equal to (5,2.321928095)\r<BR>\n" );
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document.write( "in the inverse equation, you want x to be equal to 2.321928095.\r<BR>\n" );
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document.write( "let g(x) represent the inverse equation.\r<BR>\n" );
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document.write( "your inverse equation becomes g(x) = (2^(x+2)/4.\r<BR>\n" );
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document.write( "whenb x = 2.321928095, this equation becomes g(x) = (2^(4.321928095)/4 which becomes g(x) = 5\r<BR>\n" );
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document.write( "you have (x,y) in the inverse equation is equal to (2.321928095,5)\r<BR>\n" );
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document.write( "(x,y) from the original equation is equal to (5,2.321928095)\r<BR>\n" );
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document.write( "(x,y) from the inverse equation is equal to ((2.321928095,5)\r<BR>\n" );
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document.write( "this is what they mean by (x,y) in the original equation is equal to (y,x) in the inverse equation.\r<BR>\n" );
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document.write( "the x value in the original equation becomes the y value in the inverse equation.\r<BR>\n" );
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document.write( "the y value in the original equation becomes the x value in the inverse equation.\r<BR>\n" );
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document.write( "the graph will show these equations to be reflections about the line y = x.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/032402.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the red line is the original equation of y = log2(4x) - 2.\r<BR>\n" );
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document.write( "the blue line is the inverse equation of y = 2^(x+2)/4\r<BR>\n" );
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document.write( " </SPAN>\n" );
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