document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182944>Question 1182944</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) The functions 𝑓 and 𝑔 are defined as follows. <BR>\n" );
document.write( "    𝑓(𝑥) = 3𝑥^2, where 𝑥 ∈ (−1, 1) and 𝑔(𝑥) = 𝑥 + 2, where 𝑥 ∈ (−1, 1).<BR>\n" );
document.write( "   i) Find 𝑅(𝑓) and 𝑅(𝑔).<BR>\n" );
document.write( "   ii) Draw the graphs of 𝑓 and 𝑔.<BR>\n" );
document.write( "   iii) Find 𝑓 ∘ 𝑔 and 𝑔 ∘ 𝑓.<BR>\n" );
document.write( "   iv) Show that 𝑓(𝑥) is not one to one function.\r<BR>\n" );
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document.write( " (b)  The function ℎ is defined as ℎ(𝑥) = 3𝑥^2, where 𝑥 ∈ (−∞, 0].<BR>\n" );
document.write( "     i) Show that ℎ is a one to one function. <BR>\n" );
document.write( "    ii) Find the inverse function  ℎ−1 of ℎ.<BR>\n" );
document.write( "    iii) Show that,<BR>\n" );
document.write( "          (α) ℎ−1∘ ℎ(𝑥) = 𝑥, where 𝑥 ∈ (−∞, 0].<BR>\n" );
document.write( "          (β) ℎ ∘ ℎ−1(𝑥) = 𝑥, where 𝑥 ∈ [0, ∞).<BR>\n" );
document.write( "          (γ) Are the functions ℎ−1∘ ℎ and ℎ ∘ ℎ−1the same? Explain your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813070 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( " </SPAN>\n" );
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