document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316861>Question 316861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the given function is one-to-one. If it is one-to-one, find its inverse.<BR>\n" );
document.write( "f(x) = 7x^2 + 3, x &#8805; 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #226811 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=226811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplest way to figure this out is to graph it.\r<BR>\n" );
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document.write( "The graph would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-30%2C30%2Cx%5E2+%2B+3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-30%2C30%2Cx%5E2+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can see that, for all values of x, not just positive values of x, there is only one value of y for each value of x.\r<BR>\n" );
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document.write( "This makes the equation a function.\r<BR>\n" );
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document.write( "In this graph, y = f(x) = x^2 + 3\r<BR>\n" );
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document.write( "To find the inverse of the function, you would replace y with x and x with y and then solve for y.\r<BR>\n" );
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document.write( "Your equation is y = x^2 + 3<BR>\n" );
document.write( "replace y with x and x with y to get:<BR>\n" );
document.write( "x = y^2 + 3<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = +/- sqrt(x-3)\r<BR>\n" );
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document.write( "A graph of the inverse equation would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-30%2C30%2C-10%2C10%2Csqrt%28x-3%29%2C-sqrt%28x-3%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-30%2C30%2C-10%2C10%2Csqrt%28x-3%29%2C-sqrt%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You know this is an inverse equation, because it reverses the operation.\r<BR>\n" );
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document.write( "The inverse equation only exists when x >= 0.\r<BR>\n" );
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document.write( "When x = 5, the original equation gets you 5^2 + 3 = 25 + 3 = 28\r<BR>\n" );
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document.write( "In the inverse equation, when x = 28, the inverse equation gets you sqrt(28-3) = sqrt(25) = 5.\r<BR>\n" );
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document.write( "With the original equation you go from 5 to 28.<BR>\n" );
document.write( "With the inverse equation you go from 28 to 5.\r<BR>\n" );
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document.write( "While your original equation is a function, your inverse equation is not.\r<BR>\n" );
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document.write( "In a function, every value of x must yield only 1 value of y.\r<BR>\n" );
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document.write( "If any 1 value of x yields more than 1 value of y, then the equation is not a function.\r<BR>\n" );
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document.write( "In that case, it is called a relation.\r<BR>\n" );
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