August 14th, 2013, 11:19 AM  #1 
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  Range of a function
HI, How can we find the range of the following function: However, I found its domain to be . 
August 14th, 2013, 12:39 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  Re: Range of a function
Do it in two steps. First find the range of ln(arg). If it is more than 2? in length, then the range of the sin is [1,1]. 
August 15th, 2013, 01:18 AM  #3 
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  Re: Range of a function
Range of ln(arg) is of course, R. But how it is varying with the sine function...is something I am not able to arrive at.

August 15th, 2013, 01:21 AM  #4 
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  Re: Range of a function
And when , but then how to interpret with ln(arg)?

August 15th, 2013, 12:23 PM  #5 
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  Re: Range of a function
When the domain of a sine function is the entire real line, the sine simply oscillates between 1 and 1. Therefore the range is [1,1]. I don't understand what your concern is?

August 16th, 2013, 06:56 AM  #6  
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  Re: Range of a function Quote:
 
August 16th, 2013, 07:40 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Range of a function
You need to compute the range of on the interval (2, 1), then consider the sine of that range of values.

August 16th, 2013, 08:31 AM  #8  
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  Re: Range of a function Quote:
 
August 17th, 2013, 05:32 AM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Range of a function
Yes.

August 17th, 2013, 07:31 AM  #10 
Senior Member Joined: Jan 2012 Posts: 140 Thanks: 2  Re: Range of a function
It means the answer to the original question is but the answer give in the text book is which should be misprinted, I believe...correct..?


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