document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135135>Question 1135135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> show that the given function is one-to-one and find its inverse. Check your<BR>\n" );
document.write( "answers algebraically and graphically. Verify that the range of f is the domain of f^−1 and vice-versa.\r<BR>\n" );
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document.write( "f(x) = 3√x−1 − 4  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752674 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "show that the given function is one-to-one and find its inverse. Check your<BR>\n" );
document.write( "answers algebraically and graphically. Verify that the range of f is the domain of f^−1 and vice-versa. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3sqrt%28x-1%29+-+4+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+3sqrt%28x-1%29+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It is a 1-1 function if it passes both the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertical+ ALIGN=MIDDLE  ALT=\"vertical+\"   DISABLED_style= \"max-width:90%; height:auto;\" >line test and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=horizontal ALIGN=MIDDLE  ALT=\"horizontal\"   DISABLED_style= \"max-width:90%; height:auto;\" > line test. \r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29+=f%28b%29+ ALIGN=MIDDLE  ALT=\"f%28a%29+=f%28b%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > implies that a=b, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is 1-1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%28a-1%29+-+4=+3sqrt%28b-1%29+-+4 ALIGN=MIDDLE  ALT=\"3sqrt%28a-1%29+-+4=+3sqrt%28b-1%29+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%28a-1%29+=+3sqrt%28b-1%29 ALIGN=MIDDLE  ALT=\"3sqrt%28a-1%29+=+3sqrt%28b-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a-1%29+=+sqrt%28b-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28a-1%29+=+sqrt%28b-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-1+=+b-1 ALIGN=MIDDLE  ALT=\"a-1+=+b-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b ALIGN=MIDDLE  ALT=\"a+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, your function is injective (one-to-one)\r<BR>\n" );
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document.write( "inverse:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+3sqrt%28x-1%29+-+4+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+3sqrt%28x-1%29+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+y+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+3sqrt%28x-1%29+-+4+ ALIGN=MIDDLE  ALT=\"y=+3sqrt%28x-1%29+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >......swap <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+3sqrt%28y-1%29+-+4+ ALIGN=MIDDLE  ALT=\"x=+3sqrt%28y-1%29+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4=+3sqrt%28y-1%29++ ALIGN=MIDDLE  ALT=\"x%2B4=+3sqrt%28y-1%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%2F3=+sqrt%28y-1%29++ ALIGN=MIDDLE  ALT=\"%28x%2B4%29%2F3=+sqrt%28y-1%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E-1%28x%29=%281%2F9%29%28x%5E2%2B8x%2B25%29+ ALIGN=MIDDLE  ALT=\"f%5E-1%28x%29=%281%2F9%29%28x%5E2%2B8x%2B25%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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