document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=589966>Question 589966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Decide whether or not the functions are inverses of each other.\r<BR>\n" );
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document.write( "1]  f(x)= 4x+16 and g(x)= 1/4x-4\r<BR>\n" );
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document.write( "2] f(x)= sqrt(x+8), domain [-8, infinity); g(x)=x^2+8, domain (-infinity, infinity)\r<BR>\n" );
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document.write( "and last one:\r<BR>\n" );
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document.write( "Determine <BR>\n" );
document.write( "i) the domain of the function, <BR>\n" );
document.write( "ii) the range of the function, <BR>\n" );
document.write( "iii) the domain of the inverse, and <BR>\n" );
document.write( "iv) the range of the inverse.\r<BR>\n" );
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document.write( "f(x) = 2x + 1\r<BR>\n" );
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document.write( "I need help understanding these three questions :( Inverses was my least favorite in Algebra! If you could please help, would be greatly appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #376098 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=376098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Decide whether or not the functions are inverses of each other. <BR>\n" );
document.write( "1] f(x)= 4x+16 and g(x)= 1/4x-4 <BR>\n" );
document.write( "2] f(x)= sqrt(x+8), domain [-8, infinity); g(x)=x^2+8, domain (-infinity, infinity) <BR>\n" );
document.write( "and last one: <BR>\n" );
document.write( "Determine <BR>\n" );
document.write( "i) the domain of the function, <BR>\n" );
document.write( "ii) the range of the function, <BR>\n" );
document.write( "iii) the domain of the inverse, and <BR>\n" );
document.write( "iv) the range of the inverse. <BR>\n" );
document.write( "f(x) = 2x + 1 <BR>\n" );
document.write( "**<BR>\n" );
document.write( "1] f(x)= 4x+16 and g(x)= 1/4x-4 <BR>\n" );
document.write( "(fog)(x)=f[g(x)]=4[(x/4)-4)]+16=x-16+16=x<BR>\n" );
document.write( "(gof)(x)=g[f(x)]=(1/4)(4x+16)-4=x+4-4=x<BR>\n" );
document.write( "Therefore functions are one-to-one and inverses to each other.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2] f(x)= sqrt(x+8), g(x)=x^2+8<BR>\n" );
document.write( "f(x) is a one-to-one function but g(x) is not. g(x) is a parabola which is bumped 8 units up and it would fail the horizontal line test as it would have two intersections, that is for a given y, you could have two different x's. These two functions are not inverses of each other.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "f(x)=2x+1<BR>\n" );
document.write( "i) domain:all real numbers or (-&#8734;,&#8734;)<BR>\n" );
document.write( "ii) range: (-&#8734;,&#8734;) (This is a straight line with a slope=2 and y-intercept=1.<BR>\n" );
document.write( "iii) the domain of the inverse.<BR>\n" );
document.write( "x=2y+1<BR>\n" );
document.write( "2y=x-1<BR>\n" );
document.write( "y^-1=(x-1)/2=x/2-1/2 (This is a straight line with slope=1/2 and y-intercept=-1/2)<BR>\n" );
document.write( "domain:  (-&#8734;,&#8734;) <BR>\n" );
document.write( "iv) range of inverse: (-&#8734;,&#8734;)<BR>\n" );
document.write( " </SPAN>\n" );
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