document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197653>Question 1197653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which if the following functions has domain (-1,1)and range (0,pi)<BR>\n" );
document.write( "A. f(x)=sin((pi/2)x)<BR>\n" );
document.write( "B. f(x)=arcsin(x)<BR>\n" );
document.write( "C. f(x)=cos(x)<BR>\n" );
document.write( "D. f(x)=arccos(x) </SPAN>\n" );
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document.write( "Choices A and C are immediately ruled out because their domain is \"set of all real numbers\". \r<BR>\n" );
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document.write( "The answer is one of the inverse trig functions either arcsine or arccosine.\r<BR>\n" );
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document.write( "Refer to this page<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.alamo.edu/contentassets/35e1aad11a064ee2ae161ba2ae3b2559/trigonometric/math2412-inverse-trig-functions.pdf\">https://www.alamo.edu/contentassets/35e1aad11a064ee2ae161ba2ae3b2559/trigonometric/math2412-inverse-trig-functions.pdf</a><BR>\n" );
document.write( "To see how the y = sin(x) function has its domain restricted to the interval [-pi/2, pi/2] so that it becomes one-to-one. This allows the inverse to be possible. \r<BR>\n" );
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document.write( "On the domain [-pi/2, pi/2] the corresponding range is [-1, 1]<BR>\n" );
document.write( "When computing the inverse, the domain and range swap.<BR>\n" );
document.write( "Therefore, the domain of arcsine is [-1,1] and its range is [-pi/2, pi/2]<BR>\n" );
document.write( "This rules out choice B.\r<BR>\n" );
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document.write( "You should find that y = cos(x) should have a domain restriction of [0, pi] so that we have a one-to-one portion.<BR>\n" );
document.write( "This covers a range of [-1,1]<BR>\n" );
document.write( "The domain and range swap leading arccos to have a domain of [-1,1] and range of [0,pi]<BR>\n" );
document.write( "In short, this shows why choice D is the answer.\r<BR>\n" );
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document.write( "Side note: I don't know why your teacher has excluded the endpoints. The endpoints should be included.<BR>\n" );
document.write( "Something like f(x) = 0 is possible for f(x) = arccos(x). It occurs when x = 1.\r<BR>\n" );
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document.write( "Answer: Choice D.  f(x) = arccos(x)<BR>\n" );
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