Find the domain and range of this function:

f(x) = cosx/x.

I just took a quiz today and I blanked out. I wasn't sure what notation you are supposed to use for this kind of problem so I probably got it wrong.

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- September 2nd 2011, 06:40 PMexplodingtoenailsDomain and range of this function?
Find the domain and range of this function:

f(x) = cosx/x.

I just took a quiz today and I blanked out. I wasn't sure what notation you are supposed to use for this kind of problem so I probably got it wrong. - September 2nd 2011, 08:20 PMProve ItRe: Domain and range of this function?
- September 2nd 2011, 09:10 PMexplodingtoenailsRe: Domain and range of this function?
The domain would be (-infinity, 0) U (0, infinity)?

- September 2nd 2011, 09:17 PMProve ItRe: Domain and range of this function?
- September 2nd 2011, 09:56 PMexplodingtoenailsRe: Domain and range of this function?
When the denominator is large, the number is smaller, and vice versa when the denominator is small.

Would the range be (-infinity, +infinity)?

Also, how do I know which notation to use when doing domain and range of a function? ie. The parenthetical notation or using "less than or equal to" signs? - September 2nd 2011, 10:36 PMProve ItRe: Domain and range of this function?
Yes, because for small negative values of x, the function shoots to , while for small positive values of the function shoots to . Of course, it's easier to write instead of .

All notations are equivalent, it's just personal preference (I go for whichever one is easiest to write in each case). - September 3rd 2011, 01:41 PMexplodingtoenailsRe: Domain and range of this function?
Just as an extra question, would the limit as x approaches infinity of cosx/x be infinity?

- September 3rd 2011, 01:52 PMProve ItRe: Domain and range of this function?
- September 3rd 2011, 02:08 PMexplodingtoenailsRe: Domain and range of this function?
- September 3rd 2011, 02:12 PMProve ItRe: Domain and range of this function?
I suggest you zoom out so that you get a better picture of what the function's behaviour is. It fluctuates because the cosine function fluctuates. But you should notice that they fluctuate less and less as the x values increase. Even though the function will continue to oscillate forever, as the denominator increases, the function will still get infinitesimally small so that the function is indistinguishable from 0.

- September 3rd 2011, 02:20 PMexplodingtoenailsRe: Domain and range of this function?