Question

How do you find the domain & range for `g(t)= cos (1/t)`?

Answer 1

Domain - all real numbers except zero.

The range is `-1<=g(t) <=1`

Explanation:

The domain is the set of `x` (or in this case `t`) values for which the function is valid.
In this case it doesn't matter how big or small `1/t` gets, positively or negatively, as it will still form a valid angle as long as it is a real number. Therefore `1/t` is only invalid when `t=0`

Domain - all real numbers except zero.

The range is `-1<=g(t) <=1` as cosine is always in this range.