Domain and Range question

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October 16th 2011, 09:28 AM
FelixHelix

Domain and Range question

Hi,

New to this site and hoped to get some advice with a question from first year Uni.

Find the domain and range of:

y $\f=\sin \left( \frac1{x+1} \right) + \exp \left( \frac1{x+1} \right)$

And explain if it has an inverse or not.

We've done a over view of domains and ranges but I can't see any example quite like this in any of our notes or text books.

I think the Domain is all Real numbers except x= -1 as function would not be well defined. The range, well, sine function will be [-1,1] and not sure of the exponential and when they are combined what happends. I've graphed this on Maple and don't know how to interpret the function.

Any pointers and advice would be greatly appreciated.

Thanks,

Felix
October 16th 2011, 10:01 AM
Siron

Re: Domain and Range question

You know that the domain of $\sin(x)$ is $\mathbb{R}$ , but now you have $\sin\left(\frac{1}{x+1}\right)$ therefore you have to exclude the values wherefore the denominator becomes equal to 0 (same for the exp(...)).
October 16th 2011, 10:13 AM
FelixHelix

Re: Domain and Range question

The only number that makes the denominators 0 is x = -1 as I mentioned. Is this not correct?
October 16th 2011, 10:40 AM
prime

Re: Domain and Range question

i think the domain is R-{-1}
and the range is R-[-1 ,-infinity)
October 16th 2011, 11:22 AM
mr fantastic

Quote:

Originally Posted by FelixHelix

Hi,

New to this site and hoped to get some advice with a question from first year Uni.

Find the domain and range of:

y $\f=\sin \left( \frac1{x+1} \right) + \exp \left( \frac1{x+1} \right)$

And explain if it has an inverse or not.

We've done a over view of domains and ranges but I can't see any example quite like this in any of our notes or text books.

I think the Domain is all Real numbers except x= -1 as function would not be well defined. The range, well, sine function will be [-1,1] and not sure of the exponential and when they are combined what happends. I've graphed this on Maple and don't know how to interpret the function.

Any pointers and advice would be greatly appreciated.

Thanks,

Felix

Your domain is correct. To get the range, I suggest you first attempt to sketch each function seperately (the sine and the exp) and then add the graphs together using addition of ordinates ....

Quote:

Originally Posted by prime

i think the domain is R-{-1}
and the range is R-[-1 ,-infinity)

Your range is wrong.
October 16th 2011, 11:39 AM
SammyS

Re: Domain and Range question

Also sketch the graph of 1/(x+1).

The sine & exponential functions are used with very "large" negative as well as positive numbers.