document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100228>Question 1100228</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Can someone help me? Thank you. <BR>\n" );
document.write( "Function f(x)= sin X is neither one to one nor onto function. Why?<BR>\n" );
document.write( "Determine restrictions on the domain and co-domain so that f(x)=sin x is invertible. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714892 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One to one : Since the sin function is periodic, there are multiple values of x for a given value of y. Therefore it cannot be one to one.<BR>\n" );
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document.write( "Onto : There is no x in the domain that will give a value of f(x) such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28f%28x%29%29%3E1 ALIGN=MIDDLE  ALT=\"abs%28f%28x%29%29%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it's not onto.<BR>\n" );
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document.write( "If we restrict the domain to [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29pi ALIGN=MIDDLE  ALT=\"%281%2F2%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29pi ALIGN=MIDDLE  ALT=\"%283%2F2%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >] and restrict the co-domain to [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >].<BR>\n" );
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