document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=592791>Question 592791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help and show work. Thanks in advance.\r<BR>\n" );
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document.write( "a. Does the function f(x)=x^2 have an inverse? If so, what is it? If not, why not?\r<BR>\n" );
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document.write( "b. the function f(x)= x+3/x-5 has an inverse. Please find it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #376068 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=376068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please help and show work. Thanks in advance. <BR>\n" );
document.write( "a. Does the function f(x)=x^2 have an inverse? If so, what is it? If not, why not? <BR>\n" );
document.write( "b. the function f(x)= x+3/x-5 has an inverse. Please find it.<BR>\n" );
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document.write( "The method used to find the inverse: interchange x and y, then solve for y.<BR>\n" );
document.write( "symbol used for inverse: y^-1<BR>\n" );
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document.write( "a. y=x^2<BR>\n" );
document.write( "This function does not have an inverse. If you graph this function, you will see that is is a parabola that opens upwards so for a given y you will have two different x's. This means it is not a one-to-one function and cannot have an inverse. You can also use the horizontal line test to show it will have two intersections which means the function is not one-to-one<BR>\n" );
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document.write( "b. y=(x+3)/(x-5)<BR>\n" );
document.write( "This function is one-to-one and its inverse can be found by interchanging x and y, then solving for y.<BR>\n" );
document.write( "x=(y+3)/(y-5)<BR>\n" );
document.write( "xy-5x=y+3<BR>\n" );
document.write( "xy-y=5x+3<BR>\n" );
document.write( "y(x-1)=5x+3<BR>\n" );
document.write( "y^-1=(5x+3)/(x-1) </SPAN>\n" );
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