document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012558>Question 1012558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3.26\r<BR>\n" );
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document.write( "For the function f(x)=4x-5 determine whether f(x) is one-to-one. If so, find a formula for the inverse, <BR>\n" );
document.write( "give the domain and range for f^-1 , and then graph both functions on the same axes.\r<BR>\n" );
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document.write( "1. Is f(x) a one-to-one function? Yes or No\r<BR>\n" );
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document.write( "2. The inverse function is f^-1 =\r<BR>\n" );
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document.write( "3. What is the correct range?\r<BR>\n" );
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document.write( "4.Graph for f and f^-1A: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628548 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=628548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the function f(x)=4x-5 determine whether f(x) is one-to-one. If so, find a formula for the inverse,<BR>\n" );
document.write( "give the domain and range for f^-1 , and then graph both functions on the same axes.<BR>\n" );
document.write( "1. Is f(x) a one-to-one function? Yes or No\r<BR>\n" );
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document.write( "yes - it's an equation for a straight line which is always 1 to 1.\r<BR>\n" );
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document.write( "2. The inverse function is f^-1 =\r<BR>\n" );
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document.write( "set f(x) = y and the function becomes y = 4x-5\r<BR>\n" );
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document.write( "the inverse function is x = 4y - 5\r<BR>\n" );
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document.write( "it is found by replacing y with x and x with y.\r<BR>\n" );
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document.write( "you can solve this function for y in the following manner:<BR>\n" );
document.write( "start with x = 4y - 5<BR>\n" );
document.write( "subtract x from both sides of the equation and subtract 4y from both sides of the equation to get -4y = -x - 5<BR>\n" );
document.write( "divide both sides of the equation by -4 to get y = x/4 + 5/4\r<BR>\n" );
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document.write( "x = 4y - 5 and y = x/4 + 5/4 are identical equations.<BR>\n" );
document.write( "they are both inverse equations of y = 4x - 5.\r<BR>\n" );
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document.write( "3. What is the correct range?\r<BR>\n" );
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document.write( "the domain of the original function is all real values of x.<BR>\n" );
document.write( "the range of the original function is all real values of y.\r<BR>\n" );
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document.write( "the domain of the inverse equation is the same as the range of the original function.\r<BR>\n" );
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document.write( "the range of the inverse equation is the same as the domain of the original function.\r<BR>\n" );
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document.write( "4.Graph for f and f^-1A: \r<BR>\n" );
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document.write( "graph is shown below:\r<BR>\n" );
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document.write( "the original equation is red.<BR>\n" );
document.write( "the inverse equation is blue.<BR>\n" );
document.write( "both x = 4y-5 and y = 4x+5/4 are blue.<BR>\n" );
document.write( "since these equations are identical, they show up as the same line on the graph.<BR>\n" );
document.write( "the dashed line of y = x is also shown.<BR>\n" );
document.write( "since the equations are inverses of each other, they are symmetric about the line y = x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/010602.jpg\" alt=\"$$$\" </> </SPAN>\n" );
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