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.
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?
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).
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.