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August 14th, 2013, 11:19 AM   #1
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Range of a function

HI,

How can we find the range of the following function:



However, I found its domain to be .
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August 14th, 2013, 12:39 PM   #2
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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].
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August 15th, 2013, 01:18 AM   #3
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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.
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August 15th, 2013, 01:21 AM   #4
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Re: Range of a function

And when , but then how to interpret with ln(arg)?
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August 15th, 2013, 12:23 PM   #5
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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?
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August 16th, 2013, 06:56 AM   #6
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Re: Range of a function

Quote:
Originally Posted by mathman
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?
Well, the domain of the sine function is R but then what the ln(arg) part playing the role..? Is it not affecting the range?
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August 16th, 2013, 07:40 AM   #7
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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.
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August 16th, 2013, 08:31 AM   #8
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Re: Range of a function

Quote:
Originally Posted by greg1313
You need to compute the range of on the interval (-2, 1), then consider the sine of that range of values.
Let its range be g. Then . Is it correct...?
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August 17th, 2013, 05:32 AM   #9
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Re: Range of a function

Yes.
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August 17th, 2013, 07:31 AM   #10
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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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