document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173554>Question 1173554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation used for converting degrees Celsius to degrees Fahrenheit is F=2C+30. (In function<BR>\n" );
document.write( "notation this would be f(c)=2c +30 )<BR>\n" );
document.write( "a) Find the inverse of this function.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798781 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=798781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the conversion factor you show is f = 2c + 30\r<BR>\n" );
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document.write( "to find the inverse of this function, replace f with c and c with f to get:\r<BR>\n" );
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document.write( "c = 2f + 30\r<BR>\n" );
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document.write( "you need to solve for f.\r<BR>\n" );
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document.write( "subtract 30 from both sides of the equation and then divide both side of the equation by 2 to get:\r<BR>\n" );
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document.write( "(c - 30) / 2 = f\r<BR>\n" );
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document.write( "switch sides to get:\r<BR>\n" );
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document.write( "f = (c - 30) / 2\r<BR>\n" );
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document.write( "to graph both functions, replace f with y and c with x.\r<BR>\n" );
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document.write( "the graphs looks like this:\r<BR>\n" );
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document.write( "the original equation is y = 2x + 30.<BR>\n" );
document.write( "that's in red.<BR>\n" );
document.write( "when you replace y with f and x with c, the original equation becomes:<BR>\n" );
document.write( "f = 2c + 30\r<BR>\n" );
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document.write( "the inverse equation is y = (x - 30) / 2<BR>\n" );
document.write( "that's in blue.<BR>\n" );
document.write( "when you replace y with f and x with c, the inverse equation becomes:<BR>\n" );
document.write( "f = (c - 30) / 2\r<BR>\n" );
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document.write( "the line y = x is in black.<BR>\n" );
document.write( "if the equations are inverses of each other, then they are reflections about the line y = x.\r<BR>\n" );
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document.write( "the dashed black line is y = -x + 30<BR>\n" );
document.write( "that line is used to show the points directly opposite from each other about the line y = x.<BR>\n" );
document.write( "the points are (0,30) on the original equation and (30,0) on the inverse equation.<BR>\n" );
document.write( "this confirms the lines are reflections of each other about the line y = x.\r<BR>\n" );
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document.write( "another test is to use the composite function of f(g(x)) or g(f(x)) and get the value of x.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "let f(x) = 2x + 30 and let g(x) = (x-30)/2\r<BR>\n" );
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document.write( "to get f(g(x)), replace x in f(x) with (x-30)/2 from g(x).<BR>\n" );
document.write( "you will get:<BR>\n" );
document.write( "f(g(x)) = 2 * (x-30)/2 + 30<BR>\n" );
document.write( "simplify to get:'<BR>\n" );
document.write( "f(g(x)) = 2 * x/2 - 2*30/2 + 30<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "f(g(x)) = x - 30 + 30<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "f(g(x)) = x\r<BR>\n" );
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document.write( "to get g(f(x)), replace x in g(x) with (2x + 30) from f(x).<BR>\n" );
document.write( "you will get:<BR>\n" );
document.write( "g(f(x)) = ((2x + 30) - 30) / 2<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "g(f(x)) = (2x) / 2<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "g(f(x)) = x\r<BR>\n" );
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document.write( "you got f(g(x)) = x and g(f(x)) = x<BR>\n" );
document.write( "this confirms the equations are inverse of each other.\r<BR>\n" );
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document.write( "note that, if g(x) is inverse to f(x), then g(x) can also be written as f<sup>-1</sup>(x))\r<BR>\n" );
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document.write( "here's a reference on proving that the equations are inverse of each other.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/invrsfcn7.htm\" target = \"_blank\">https://www.purplemath.com/modules/invrsfcn7.htm</a> </SPAN>\n" );
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